MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f8(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) -> Com_1(f32(Ar_0, Ar_1, Fresh_23, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) f15(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) -> Com_1(f8(Ar_0, Ar_1, Ar_2, Fresh_22, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12)) (Comp: ?, Cost: 1) f300(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) -> Com_1(f8(Ar_0 + 1, 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_1 >= Ar_4 ] (Comp: ?, Cost: 1) f8(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) -> Com_1(f8(Ar_0 + 1, 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_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: ?, Cost: 1) f13(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) -> Com_1(f1(Ar_0, Ar_1, Fresh_19, Ar_3, Ar_4, Fresh_20, Fresh_21, 0, -2, 0, 0, Ar_11, Ar_12)) (Comp: ?, Cost: 1) f12(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) -> Com_1(f1(Ar_0, Ar_1, Fresh_16, Ar_3, Ar_4, Fresh_17, Fresh_18, 0, Ar_8, 0, 0, Ar_8 - 1, Ar_12)) [ 4 >= Ar_8 ] (Comp: ?, Cost: 1) f10(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) -> Com_1(f1(Ar_0, Ar_1, Fresh_13, Ar_3, Ar_4, Fresh_14, Fresh_15, 0, Ar_8, 0, 0, Ar_11, -2)) (Comp: ?, Cost: 1) f8(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) -> Com_1(f1(Ar_0, Ar_1, Fresh_10, Ar_3, Ar_4, Fresh_11, Fresh_12, 0, Ar_8, 0, 0, Ar_11, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(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) -> Com_1(f1(Ar_0, Ar_1, Fresh_7, Ar_3, Ar_4, Fresh_8, Fresh_9, 0, Ar_8, 0, 0, Ar_11, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: ?, Cost: 1) f300(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) -> Com_1(f1(Ar_0, Ar_1, Fresh_4, Ar_3, Ar_4, Fresh_5, Fresh_6, 0, Ar_8, 0, 0, Ar_11, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f12(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) -> Com_1(f300(Ar_0, Ar_1 + 1, Fresh_2, Ar_3, Ar_4, Fresh_3, Ar_6, 1, Ar_8, 1, 1, Ar_11, Ar_12)) [ Ar_8 >= 5 ] (Comp: ?, Cost: 1) f1(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) -> Com_1(f300(Ar_0, Ar_1 + 1, Fresh_0, Ar_3, Ar_4, Fresh_1, Ar_6, 1, Ar_8, 1, 1, Ar_11, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (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) -> Com_1(f15(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)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1, Ar_4, Ar_8, Ar_12]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_8, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_8, Ar_12)) [ Ar_8 >= 5 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, -2)) (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ 4 >= Ar_8 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, -2, Ar_12)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_1 >= Ar_4 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_0 >= Ar_1 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 2: f12(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_8, Ar_12)) [ Ar_8 >= 5 ] f10(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, -2)) f12(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ 4 >= Ar_8 ] f13(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, -2, Ar_12)) We thus obtain the following problem: 3: T: (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_1 >= Ar_4 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_8, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_8, Ar_12)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12)) (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(f15) = 1 Pol(f8) = 1 Pol(f1) = 1 Pol(f32) = 0 Pol(f300) = 1 orients all transitions weakly and the transition f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12)) (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f8) = 0 Pol(f300) = 1 Pol(f1) = 1 and size complexities S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ]", 0-0) = Ar_0 + 1 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ]", 0-1) = ? S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ]", 0-2) = Ar_4 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ]", 0-3) = Ar_12 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ]", 0-1) = ? S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ]", 0-2) = Ar_4 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ]", 0-3) = Ar_12 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ 4 >= Ar_12 ]", 0-0) = Ar_0 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ 4 >= Ar_12 ]", 0-1) = ? S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ 4 >= Ar_12 ]", 0-2) = Ar_4 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ 4 >= Ar_12 ]", 0-3) = Ar_12 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ Ar_12 >= 5 ]", 0-0) = Ar_0 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ Ar_12 >= 5 ]", 0-1) = ? S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ Ar_12 >= 5 ]", 0-2) = Ar_4 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ Ar_12 >= 5 ]", 0-3) = Ar_12 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ]", 0-0) = ? S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ]", 0-1) = ? S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ]", 0-2) = Ar_4 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ]", 0-3) = Ar_12 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_1 >= Ar_4 ]", 0-0) = ? S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_1 >= Ar_4 ]", 0-1) = ? S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_1 >= Ar_4 ]", 0-2) = Ar_4 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_1 >= Ar_4 ]", 0-3) = Ar_12 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_4 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_4 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_4 >= Ar_1 + 1 ]", 0-2) = Ar_4 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_4 >= Ar_1 + 1 ]", 0-3) = Ar_12 S("f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12))", 0-0) = Ar_0 S("f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12))", 0-1) = Ar_1 S("f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12))", 0-2) = Ar_4 S("f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12))", 0-3) = Ar_12 S("koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ]", 0-2) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ]", 0-3) = Ar_12 orients the transitions f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ] f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] weakly and the transition f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12)) (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -3*V_2 + 3*V_3 Pol(f15) = -3*V_2 + 3*V_3 Pol(f8) = -3*V_2 + 3*V_3 - 2 Pol(f1) = -3*V_2 + 3*V_3 - 2 Pol(f32) = -3*V_1 + 3*V_3 - 2 Pol(f300) = -3*V_2 + 3*V_3 - 1 orients all transitions weakly and the transitions f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12)) (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1 + 3*Ar_4, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: 3*Ar_1 + 3*Ar_4, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f8) = -V_1 + V_2 Pol(f1) = 0 and size complexities S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ]", 0-0) = Ar_0 + 1 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ]", 0-1) = 4*Ar_1 + 4*Ar_4 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ]", 0-2) = Ar_4 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ]", 0-3) = Ar_12 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ]", 0-1) = 4*Ar_1 + 4*Ar_4 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ]", 0-2) = Ar_4 S("f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ]", 0-3) = Ar_12 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ 4 >= Ar_12 ]", 0-0) = Ar_0 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ 4 >= Ar_12 ]", 0-1) = 4*Ar_1 + 4*Ar_4 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ 4 >= Ar_12 ]", 0-2) = Ar_4 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ 4 >= Ar_12 ]", 0-3) = Ar_12 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ Ar_12 >= 5 ]", 0-0) = Ar_0 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ Ar_12 >= 5 ]", 0-1) = 4*Ar_1 + 4*Ar_4 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ Ar_12 >= 5 ]", 0-2) = Ar_4 S("f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\\ Ar_12 >= 5 ]", 0-3) = Ar_12 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ]", 0-0) = ? S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ]", 0-1) = 4*Ar_1 + 4*Ar_4 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ]", 0-2) = Ar_4 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ]", 0-3) = Ar_12 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_1 >= Ar_4 ]", 0-0) = ? S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_1 >= Ar_4 ]", 0-1) = 4*Ar_1 + 4*Ar_4 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_1 >= Ar_4 ]", 0-2) = Ar_4 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_1 >= Ar_4 ]", 0-3) = Ar_12 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_4 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_4 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_4 >= Ar_1 + 1 ]", 0-2) = Ar_4 S("f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\\ Ar_4 >= Ar_1 + 1 ]", 0-3) = Ar_12 S("f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12))", 0-0) = Ar_0 S("f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12))", 0-1) = Ar_1 S("f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12))", 0-2) = Ar_4 S("f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12))", 0-3) = Ar_12 S("koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ]", 0-2) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ]", 0-3) = Ar_12 orients the transitions f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] weakly and the transition f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12)) (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: 2*Ar_0 + 5*Ar_1 + 4*Ar_4 + 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1 + 3*Ar_4, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: 3*Ar_1 + 3*Ar_4, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_4 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_4 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 8 to obtain the following invariants: For symbol f1: -X_2 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ -X_1 + X_2 - 1 >= 0 For symbol f300: X_4 - 5 >= 0 /\ -X_2 + X_3 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 This yielded the following problem: 9: T: (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_12 - 5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_1 >= Ar_4 ] (Comp: 3*Ar_1 + 3*Ar_4, Cost: 1) f300(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_12 - 5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_4 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 2 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_4 >= Ar_1 + 1 /\ 4 >= Ar_12 ] (Comp: 3*Ar_1 + 3*Ar_4, Cost: 1) f1(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f300(Ar_0, Ar_1 + 1, Ar_4, Ar_12)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 2 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_4 >= Ar_1 + 1 /\ Ar_12 >= 5 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f32(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_0 >= Ar_1 ] (Comp: 2*Ar_0 + 5*Ar_1 + 4*Ar_4 + 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0 + 1, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_1 >= Ar_4 ] (Comp: 1, Cost: 1) f8(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f1(Ar_0, Ar_1, Ar_4, Ar_12)) [ Ar_1 >= Ar_0 + 1 /\ Ar_4 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f15(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f8(Ar_0, Ar_1, Ar_4, Ar_12)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_4, Ar_12) -> Com_1(f15(Ar_0, Ar_1, Ar_4, Ar_12)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 2.386 sec (SMT: 2.282 sec)