WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(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) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2start) = 2 Pol(evalwcet2entryin) = 2 Pol(evalwcet2bb5in) = 2 Pol(evalwcet2bb2in) = 2 Pol(evalwcet2returnin) = 1 Pol(evalwcet2bb1in) = 2 Pol(evalwcet2bb4in) = 2 Pol(evalwcet2stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2start) = -2*V_1 + 9 Pol(evalwcet2entryin) = -2*V_1 + 9 Pol(evalwcet2bb5in) = -2*V_1 + 9 Pol(evalwcet2bb2in) = -2*V_1 + 8 Pol(evalwcet2returnin) = -2*V_1 + 9 Pol(evalwcet2bb1in) = -2*V_1 + 8 Pol(evalwcet2bb4in) = -2*V_1 + 8 Pol(evalwcet2stop) = -2*V_1 + 9 Pol(koat_start) = -2*V_1 + 9 orients all transitions weakly and the transition evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2bb4in) = 0 Pol(evalwcet2bb5in) = -1 Pol(evalwcet2bb2in) = 1 Pol(evalwcet2bb1in) = 1 and size complexities S("koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1 S("evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1))", 0-0) = ? S("evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1))", 0-1) = ? S("evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1))", 0-0) = ? S("evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1))", 0-1) = ? S("evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1))", 0-0) = ? S("evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1))", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ]", 0-0) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ]", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ]", 0-0) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ]", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\\ 9 >= Ar_1 ]", 0-0) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\\ 9 >= Ar_1 ]", 0-1) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ]", 0-0) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ]", 0-1) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ]", 0-0) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ]", 0-1) = 0 S("evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1))", 0-1) = Ar_1 S("evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1))", 0-1) = Ar_1 orients the transitions evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) weakly and the transition evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2bb4in) = 1 Pol(evalwcet2bb5in) = 0 Pol(evalwcet2bb2in) = 2 Pol(evalwcet2bb1in) = 2 and size complexities S("koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1 S("evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1))", 0-0) = ? S("evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1))", 0-1) = ? S("evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1))", 0-0) = ? S("evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1))", 0-1) = ? S("evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1))", 0-0) = ? S("evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1))", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ]", 0-0) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ]", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ]", 0-0) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ]", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\\ 9 >= Ar_1 ]", 0-0) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\\ 9 >= Ar_1 ]", 0-1) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ]", 0-0) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ]", 0-1) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ]", 0-0) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ]", 0-1) = 0 S("evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1))", 0-1) = Ar_1 S("evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1))", 0-1) = Ar_1 orients the transitions evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) weakly and the transition evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: 6*Ar_0 + 27, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2bb2in) = 1 Pol(evalwcet2bb4in) = 0 Pol(evalwcet2bb1in) = 1 and size complexities S("koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1 S("evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1))", 0-0) = 7*Ar_0 + 64827 S("evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1))", 0-1) = ? S("evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1))", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1))", 0-1) = ? S("evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1))", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1))", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ]", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ]", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ]", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ]", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\\ 9 >= Ar_1 ]", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\\ 9 >= Ar_1 ]", 0-1) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ]", 0-0) = 7*Ar_0 + 9261 S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ]", 0-1) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ]", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ]", 0-1) = 0 S("evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1))", 0-1) = Ar_1 S("evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1))", 0-1) = Ar_1 orients the transitions evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) weakly and the transition evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: 6*Ar_0 + 27, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2bb2in) = -2*V_2 + 19 Pol(evalwcet2bb1in) = -2*V_2 + 18 and size complexities S("koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1 S("evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1))", 0-0) = 7*Ar_0 + 64827 S("evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1))", 0-1) = ? S("evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1))", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1))", 0-1) = ? S("evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1))", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1))", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ]", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ]", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ]", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ]", 0-1) = ? S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\\ 9 >= Ar_1 ]", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\\ 9 >= Ar_1 ]", 0-1) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ]", 0-0) = 7*Ar_0 + 9261 S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ]", 0-1) = ? S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ]", 0-0) = 7*Ar_0 + 1323 S("evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ]", 0-1) = 0 S("evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1))", 0-1) = Ar_1 S("evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1))", 0-1) = Ar_1 orients the transitions evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) weakly and the transition evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: 38*Ar_0 + 171, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: 6*Ar_0 + 27, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 8 produces the following problem: 9: T: (Comp: 1, Cost: 1) evalwcet2start(Ar_0, Ar_1) -> Com_1(evalwcet2entryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalwcet2entryin(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0, Ar_1)) (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, 0)) [ 4 >= Ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb5in(Ar_0, Ar_1) -> Com_1(evalwcet2returnin(Ar_0, Ar_1)) [ Ar_0 >= 5 ] (Comp: 38*Ar_0 + 171, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb1in(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ 9 >= Ar_1 ] (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ 2 >= Ar_0 ] (Comp: 2*Ar_0 + 9, Cost: 1) evalwcet2bb2in(Ar_0, Ar_1) -> Com_1(evalwcet2bb4in(Ar_0, Ar_1)) [ Ar_1 >= 10 ] (Comp: 38*Ar_0 + 171, Cost: 1) evalwcet2bb1in(Ar_0, Ar_1) -> Com_1(evalwcet2bb2in(Ar_0, Ar_1 + 1)) (Comp: 6*Ar_0 + 27, Cost: 1) evalwcet2bb4in(Ar_0, Ar_1) -> Com_1(evalwcet2bb5in(Ar_0 + 1, Ar_1)) (Comp: 2, Cost: 1) evalwcet2returnin(Ar_0, Ar_1) -> Com_1(evalwcet2stop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalwcet2start(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 88*Ar_0 + 402 Time: 0.710 sec (SMT: 0.675 sec)