WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, 0, Ar_12, Ar_13)) [ 1 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, 1, Ar_4, Ar_5, Ar_6, 0, Ar_8, 2, Ar_10, 0, Ar_12, Ar_13)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, 1, Ar_4, Ar_5, Ar_6, 1, Ar_8, 2, Ar_10, 0, Ar_12, Ar_13)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl13(Ar_0, Ar_11, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11 + 1, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_0 >= Ar_3 + 1 /\ Ar_13 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_9 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_9, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_7 + 2 >= Ar_0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_7 + 1 /\ Ar_11 + 1 = Ar_0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 + 1 = Ar_0 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11 + 1, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_6, Ar_6, Ar_8, Ar_8, Ar_10, Ar_10, Ar_12, Ar_12, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ 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) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, 0, Ar_12, Ar_13)) [ 1 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, 1, Ar_4, Ar_5, Ar_6, 0, Ar_8, 2, Ar_10, 0, Ar_12, Ar_13)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, 1, Ar_4, Ar_5, Ar_6, 1, Ar_8, 2, Ar_10, 0, Ar_12, Ar_13)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl13(Ar_0, Ar_11, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11 + 1, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_0 >= Ar_3 + 1 /\ Ar_13 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_9 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_9, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_7 + 2 >= Ar_0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_7 + 1 /\ Ar_11 + 1 = Ar_0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 + 1 = Ar_0 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11 + 1, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_6, Ar_6, Ar_8, Ar_8, Ar_10, Ar_10, Ar_12, Ar_12, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = 1 Pol(stop) = 0 Pol(lbl53) = 1 Pol(lbl91) = 1 Pol(lbl13) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_7 + 2 >= Ar_0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_7 + 1 /\ Ar_11 + 1 = Ar_0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 + 1 = Ar_0 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, 0, Ar_12, Ar_13)) [ 1 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, 1, Ar_4, Ar_5, Ar_6, 0, Ar_8, 2, Ar_10, 0, Ar_12, Ar_13)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, 1, Ar_4, Ar_5, Ar_6, 1, Ar_8, 2, Ar_10, 0, Ar_12, Ar_13)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl13(Ar_0, Ar_11, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11 + 1, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_0 >= Ar_3 + 1 /\ Ar_13 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_9 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: ?, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_9, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: 1, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_7 + 2 >= Ar_0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_7 + 1 /\ Ar_11 + 1 = Ar_0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 + 1 = Ar_0 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: ?, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11 + 1, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_6, Ar_6, Ar_8, Ar_8, Ar_10, Ar_10, Ar_12, Ar_12, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = 3*V_1 Pol(stop) = 3*V_1 - 3*V_12 Pol(lbl53) = 3*V_1 - V_4 - 2*V_12 Pol(lbl91) = 3*V_1 - V_4 - 2*V_12 - 1 Pol(lbl13) = 3*V_1 - 3*V_12 Pol(start0) = 3*V_1 Pol(koat_start) = 3*V_1 orients all transitions weakly and the transitions lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl13(Ar_0, Ar_11, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11 + 1, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_0 >= Ar_3 + 1 /\ Ar_13 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_9 = Ar_0 ] lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_9 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_9, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11 + 1, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, 0, Ar_12, Ar_13)) [ 1 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, 1, Ar_4, Ar_5, Ar_6, 0, Ar_8, 2, Ar_10, 0, Ar_12, Ar_13)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, 1, Ar_4, Ar_5, Ar_6, 1, Ar_8, 2, Ar_10, 0, Ar_12, Ar_13)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_8 /\ Ar_9 = Ar_10 /\ Ar_11 = Ar_12 /\ Ar_13 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl13(Ar_0, Ar_11, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11 + 1, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_0 >= Ar_3 + 1 /\ Ar_13 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_9 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_9 = Ar_0 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_9, Ar_4, Ar_5, Ar_6, Ar_9, Ar_8, Ar_9 + 1, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_9 + 1 /\ Ar_3 >= Ar_7 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_9 /\ Ar_9 >= Ar_3 + 1 /\ Ar_7 + 1 >= Ar_3 /\ Ar_11 + 1 = Ar_3 /\ Ar_13 = Ar_0 ] (Comp: 1, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_7 + 2 >= Ar_0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_7 + 1 /\ Ar_11 + 1 = Ar_0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 + 1 = Ar_0 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(lbl53(Ar_0, Ar_1, Ar_2, Ar_11 + 1, Ar_4, Ar_5, Ar_6, Ar_11 + 1, Ar_8, Ar_11 + 2, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_7 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_1 + 1 >= Ar_7 /\ Ar_11 = Ar_1 + 1 /\ Ar_3 = Ar_1 + 1 /\ Ar_13 = Ar_0 /\ Ar_9 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_6, Ar_6, Ar_8, Ar_8, Ar_10, Ar_10, Ar_12, Ar_12, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 18*Ar_0 + 5 Time: 3.984 sec (SMT: 3.773 sec)