MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f20(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) -> Com_1(f28(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)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f40(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) -> Com_1(f40(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)) (Comp: ?, Cost: 1) f42(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) -> Com_1(f45(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)) (Comp: ?, Cost: 1) f28(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) -> Com_1(f40(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_0 >= 1 ] (Comp: ?, Cost: 1) f28(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) -> Com_1(f40(Ar_0, Ar_1, 0, Fresh_5, Fresh_5, Fresh_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_5 ] (Comp: ?, Cost: 1) f28(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) -> Com_1(f40(1, Ar_1, 0, Fresh_4, Fresh_4, Fresh_4, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 0 >= Ar_0 /\ Fresh_4 >= Ar_1 + 1000 ] (Comp: ?, Cost: 1) f20(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) -> Com_1(f28(0, Fresh_3, Ar_2, Ar_3, Ar_4, Ar_5, 0, Fresh_3, Fresh_3, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 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) -> Com_1(f20(1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Fresh_2, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 0 >= Fresh_2 ] (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) -> Com_1(f20(1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, 0, 1, Fresh_1, Fresh_1, Fresh_1, Fresh_1)) [ Fresh_1 >= 1 /\ Q >= 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) -> Com_1(f40(1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, 0, 1, Fresh_0, Fresh_0, Fresh_0, Fresh_0)) [ 0 >= Fresh_0 /\ Q >= 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) -> 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)) [ 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]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f40(1, Ar_1)) [ 0 >= Fresh_0 /\ Q >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f20(1, Ar_1)) [ Fresh_1 >= 1 /\ Q >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f20(1, Ar_1)) [ 0 >= Fresh_2 ] (Comp: ?, Cost: 1) f20(Ar_0, Ar_1) -> Com_1(f28(0, Fresh_3)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(1, Ar_1)) [ 0 >= Ar_0 /\ Fresh_4 >= Ar_1 + 1000 ] (Comp: ?, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) [ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_5 ] (Comp: ?, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f42(Ar_0, Ar_1) -> Com_1(f45(Ar_0, Ar_1)) (Comp: ?, Cost: 1) f40(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) (Comp: ?, Cost: 1) f20(Ar_0, Ar_1) -> Com_1(f28(Ar_0, Ar_1)) [ 0 >= Ar_0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 2: f28(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) [ Ar_0 >= 1 ] f42(Ar_0, Ar_1) -> Com_1(f45(Ar_0, Ar_1)) f20(Ar_0, Ar_1) -> Com_1(f28(Ar_0, Ar_1)) [ 0 >= Ar_0 ] We thus obtain the following problem: 3: T: (Comp: ?, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) [ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_5 ] (Comp: ?, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(1, Ar_1)) [ 0 >= Ar_0 /\ Fresh_4 >= Ar_1 + 1000 ] (Comp: ?, Cost: 1) f20(Ar_0, Ar_1) -> Com_1(f28(0, Fresh_3)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f40(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f20(1, Ar_1)) [ 0 >= Fresh_2 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f20(1, Ar_1)) [ Fresh_1 >= 1 /\ Q >= 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f40(1, Ar_1)) [ 0 >= Fresh_0 /\ Q >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: 2, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) [ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_5 ] (Comp: 2, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(1, Ar_1)) [ 0 >= Ar_0 /\ Fresh_4 >= Ar_1 + 1000 ] (Comp: 2, Cost: 1) f20(Ar_0, Ar_1) -> Com_1(f28(0, Fresh_3)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f40(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f20(1, Ar_1)) [ 0 >= Fresh_2 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f20(1, Ar_1)) [ Fresh_1 >= 1 /\ Q >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f40(1, Ar_1)) [ 0 >= Fresh_0 /\ Q >= 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol f20: -X_1 + 1 >= 0 /\ X_1 - 1 >= 0 For symbol f28: -X_1 >= 0 /\ X_1 >= 0 For symbol f40: -X_1 + 1 >= 0 /\ X_1 >= 0 This yielded the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f40(1, Ar_1)) [ 0 >= Fresh_0 /\ Q >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f20(1, Ar_1)) [ Fresh_1 >= 1 /\ Q >= 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1) -> Com_1(f20(1, Ar_1)) [ 0 >= Fresh_2 ] (Comp: ?, Cost: 1) f40(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) [ -Ar_0 + 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) f20(Ar_0, Ar_1) -> Com_1(f28(0, Fresh_3)) [ -Ar_0 + 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 1 ] (Comp: 2, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(1, Ar_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_0 /\ Fresh_4 >= Ar_1 + 1000 ] (Comp: 2, Cost: 1) f28(Ar_0, Ar_1) -> Com_1(f40(Ar_0, Ar_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_5 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 1.312 sec (SMT: 1.268 sec)