WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 /\ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) [ 0 >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) [ 0 >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 /\ E >= 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) [ 0 >= 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) [ 0 >= 1 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx1bb5in) = 2 Pol(evalEx1bb6in) = 2 Pol(evalEx1bb1in) = 2 Pol(evalEx1bb4in) = 2 Pol(evalEx1returnin) = 1 Pol(evalEx1stop) = 0 Pol(evalEx1bbin) = 2 Pol(evalEx1entryin) = 2 Pol(evalEx1start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx1bb5in) = -4*V_1 + 4*V_4 - 1 Pol(evalEx1bb6in) = -4*V_1 + 4*V_2 + 2 Pol(evalEx1bb1in) = -4*V_1 + 4*V_4 Pol(evalEx1bb4in) = -4*V_1 + 4*V_4 Pol(evalEx1returnin) = -4*V_1 + 4*V_2 + 2 Pol(evalEx1stop) = -4*V_1 + 4*V_2 + 2 Pol(evalEx1bbin) = -4*V_1 + 4*V_2 + 1 Pol(evalEx1entryin) = 4*V_1 + 2 Pol(evalEx1start) = 4*V_1 + 2 Pol(koat_start) = 4*V_1 + 2 orients all transitions weakly and the transition evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: ?, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx1bb5in) = 1 Pol(evalEx1bb6in) = 0 Pol(evalEx1bb4in) = 2 Pol(evalEx1bb1in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-0) = 0 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-1) = Ar_0 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-0) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-1) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-2) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1))", 0-0) = ? S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1))", 0-1) = ? S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1))", 0-2) = ? S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1))", 0-3) = ? S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-0) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-1) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-2) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-3) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ]", 0-0) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ]", 0-1) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ]", 0-2) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ]", 0-3) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ]", 0-0) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ]", 0-1) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ]", 0-2) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ]", 0-3) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ]", 0-0) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ]", 0-1) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ]", 0-2) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ]", 0-3) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = ? S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3))", 0-0) = ? S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3))", 0-1) = ? S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3))", 0-2) = ? S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3))", 0-3) = ? orients the transitions evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] weakly and the transition evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) strictly and produces the following problem: 7: T: (Comp: 8*Ar_0 + 4, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx1bb4in) = 1 Pol(evalEx1bb5in) = 0 Pol(evalEx1bb1in) = 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-0) = 0 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-1) = Ar_0 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = 8*Ar_0 + 256 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-0) = 8*Ar_0 + 2048 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-1) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-2) = ? S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1))", 0-0) = 8*Ar_0 + 256 S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1))", 0-1) = ? S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1))", 0-2) = 8*Ar_0 + 2056 S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1))", 0-3) = ? S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 8*Ar_0 + 16384 S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-0) = 8*Ar_0 + 256 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-1) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-2) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-3) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ]", 0-0) = 8*Ar_0 + 256 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ]", 0-1) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ]", 0-2) = ? S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ]", 0-3) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ]", 0-0) = 8*Ar_0 + 256 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ]", 0-1) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ]", 0-2) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ]", 0-3) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ]", 0-0) = 8*Ar_0 + 256 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ]", 0-1) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ]", 0-2) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ]", 0-3) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = 8*Ar_0 + 256 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = ? S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3))", 0-0) = 8*Ar_0 + 256 S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3))", 0-1) = ? S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3))", 0-2) = ? S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3))", 0-3) = ? orients the transitions evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] weakly and the transition evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] strictly and produces the following problem: 8: T: (Comp: 8*Ar_0 + 4, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ 0 >= E + 1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 8 to obtain the following invariants: For symbol evalEx1bb1in: X_2 - X_4 >= 0 /\ X_4 - 2 >= 0 /\ X_3 + X_4 - 3 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 4 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ -X_1 + X_4 - 2 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalEx1bb4in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalEx1bb5in: X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalEx1bb6in: X_1 >= 0 For symbol evalEx1bbin: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalEx1returnin: X_1 - X_2 >= 0 /\ X_1 >= 0 This yielded the following problem: 9: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_2 + 1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_0 + 4, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_1 Pol(evalEx1start) = V_1 Pol(evalEx1entryin) = V_1 Pol(evalEx1bb6in) = V_2 Pol(evalEx1bbin) = V_2 Pol(evalEx1returnin) = V_2 Pol(evalEx1bb4in) = V_4 Pol(evalEx1stop) = V_2 Pol(evalEx1bb1in) = V_4 Pol(evalEx1bb5in) = V_4 orients all transitions weakly and the transitions evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ E >= 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ 0 >= E + 1 ] strictly and produces the following problem: 10: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_2 + 1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 ] (Comp: Ar_0, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ 0 >= E + 1 ] (Comp: Ar_0, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_0 + 4, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx1bb4in) = -7*V_3 + 7*V_4 - 6 Pol(evalEx1bb1in) = -7*V_3 + 7*V_4 - 12 and size complexities S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_0 S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_0 S("evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ E >= 1 ]", 0-0) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ E >= 1 ]", 0-1) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ E >= 1 ]", 0-2) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ E >= 1 ]", 0-3) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= E + 1 ]", 0-0) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= E + 1 ]", 0-1) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= E + 1 ]", 0-2) = Ar_0 S("evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 2 >= 0 /\\ Ar_2 + Ar_3 - 3 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 4 >= 0 /\\ Ar_0 + Ar_3 - 2 >= 0 /\\ -Ar_0 + Ar_3 - 2 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= E + 1 ]", 0-3) = Ar_0 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_3 ]", 0-0) = Ar_0 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_3 ]", 0-1) = Ar_0 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_3 ]", 0-2) = Ar_0 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_3 ]", 0-3) = Ar_0 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= Ar_2 + 1 ]", 0-1) = Ar_0 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= Ar_2 + 1 ]", 0-2) = Ar_0 S("evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= Ar_2 + 1 ]", 0-3) = Ar_0 S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_0 S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_0 + Ar_2 S("evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = Ar_0 + Ar_3 S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_0 S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_0 S("evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = Ar_0 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-0) = Ar_0 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-1) = Ar_0 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-2) = Ar_0 + Ar_2 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-3) = Ar_0 + Ar_3 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_0 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-2) = Ar_0 + Ar_2 S("evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-3) = Ar_0 + Ar_3 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-0) = 0 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-1) = Ar_0 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_2 + 1 ] evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] weakly and the transition evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_2 + 1 ] strictly and produces the following problem: 11: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 84*Ar_0^2 + 64*Ar_0 + 12, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_2 + 1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 ] (Comp: Ar_0, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ 0 >= E + 1 ] (Comp: Ar_0, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ E >= 1 ] (Comp: ?, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_0 + 4, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 11 produces the following problem: 12: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalEx1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(0, Ar_0, Ar_2, Ar_3)) (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalEx1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalEx1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 84*Ar_0^2 + 64*Ar_0 + 12, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_2 + 1 ] (Comp: 4*Ar_0 + 2, Cost: 1) evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 ] (Comp: Ar_0, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ 0 >= E + 1 ] (Comp: Ar_0, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ E >= 1 ] (Comp: 84*Ar_0^2 + 64*Ar_0 + 12, Cost: 1) evalEx1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ Ar_0 + Ar_3 - 2 >= 0 /\ -Ar_0 + Ar_3 - 2 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_0 + 4, Cost: 1) evalEx1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx1bb6in(Ar_0 + 1, Ar_3, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 150*Ar_0 + 168*Ar_0^2 + 40 Time: 3.896 sec (SMT: 3.734 sec)