MAYBE Initial complexity problem: 1: T: (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, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f47(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) f39(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f47(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ Ar_2 >= 3 ] (Comp: ?, Cost: 1) f39(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f47(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ 1 >= Ar_2 ] (Comp: ?, Cost: 1) f54(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f54(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) (Comp: ?, Cost: 1) f56(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f59(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) (Comp: ?, Cost: 1) f47(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) f47(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3, 0, 0, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) f39(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f47(Ar_0, Ar_1, 2, Ar_3, Ar_4 + 1, Ar_5, Ar_7, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ Ar_2 = 2 ] (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, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_16, Fresh_17, Fresh_18, Fresh_19, Ar_4, Fresh_16, Fresh_16, Fresh_16, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (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, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_12, Fresh_13, Fresh_14, Fresh_15, Ar_4, Fresh_12, Fresh_12, Fresh_12, Fresh_12, Ar_17, 0, Fresh_11, Fresh_11, Fresh_11, 0, Ar_22)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] (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, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_7, Fresh_8, Fresh_9, Fresh_10, Ar_4, Fresh_7, Fresh_7, Fresh_7, Fresh_7, Ar_17, 0, Fresh_6, Fresh_6, Fresh_6, 0, Ar_22)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] (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, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3, Ar_4, Ar_5, Ar_6, Fresh_2, Fresh_3, Fresh_4, Fresh_5, Ar_4, Fresh_2, Fresh_2, Fresh_2, Fresh_2, Ar_17, Ar_17, 1, 1, 1, 0, Ar_22)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f0(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_1, Ar_4, 0, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, 0)) [ 0 >= Fresh_1 ] (Comp: ?, Cost: 1) f0(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_0, Ar_4, 0, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, 0)) [ Fresh_0 >= 1 ] (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, Ar_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22) -> Com_1(f0(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_14, Ar_15, Ar_16, Ar_17, Ar_18, Ar_19, Ar_20, Ar_21, Ar_22)) [ 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_2, Ar_3]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Fresh_0 >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_1)) [ 0 >= Fresh_1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, 2, Ar_3)) [ Ar_2 = 2 ] (Comp: ?, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) f56(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f59(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f54(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 2: f56(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f59(Ar_0, Ar_1, Ar_2, Ar_3)) We thus obtain the following problem: 3: T: (Comp: ?, Cost: 1) f54(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 3 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, 2, Ar_3)) [ Ar_2 = 2 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_1)) [ 0 >= Fresh_1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Fresh_0 >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: ?, Cost: 1) f54(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 3 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, 2, Ar_3)) [ Ar_2 = 2 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_1)) [ 0 >= Fresh_1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Fresh_0 >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f54) = 0 Pol(f47) = 1 Pol(f39) = 2 Pol(f13) = 3 Pol(f0) = 3 Pol(koat_start) = 3 orients all transitions weakly and the transitions f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 ] f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ] f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 3 ] f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) f54(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 3 ] (Comp: ?, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, 2, Ar_3)) [ Ar_2 = 2 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_1)) [ 0 >= Fresh_1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Fresh_0 >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(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) f54(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 3 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, 2, Ar_3)) [ Ar_2 = 2 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_1)) [ 0 >= Fresh_1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Fresh_0 >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f54) = -V_1 + V_2 Pol(f47) = -V_1 + V_2 Pol(f39) = -V_1 + V_2 Pol(f13) = -V_1 + V_2 Pol(f0) = -V_1 + V_2 Pol(koat_start) = -V_1 + V_2 orients all transitions weakly and the transition f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 7: T: (Comp: ?, Cost: 1) f54(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 3 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, 2, Ar_3)) [ Ar_2 = 2 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] (Comp: Ar_0 + Ar_1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_1)) [ 0 >= Fresh_1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Fresh_0 >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 7 to obtain the following invariants: For symbol f39: -X_1 + X_2 - 1 >= 0 This yielded the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Fresh_0 >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Fresh_1)) [ 0 >= Fresh_1 ] (Comp: Ar_0 + Ar_1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f13(Ar_0 + 1, Ar_1, 1, Ar_3)) [ 0 >= Fresh_2 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_6, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_7 /\ 0 >= Fresh_6 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f39(Ar_0, Ar_1, Fresh_11, Ar_3)) [ Ar_1 >= Ar_0 + 1 /\ 0 >= Fresh_12 /\ Fresh_11 >= 2 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Fresh_16 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 + Ar_1 - 1 >= 0 /\ 1 >= Ar_2 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, 2, Ar_3)) [ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_2 = 2 ] (Comp: 3, Cost: 1) f39(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f47(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_2 >= 3 ] (Comp: 3, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 ] (Comp: 3, Cost: 1) f47(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) f54(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f54(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 3.126 sec (SMT: 3.002 sec)