/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 2193 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y)) :|: v_.0 > 0 && v_.01 > 0 eval_foo_bb1_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.0, v_.01, v_.2, v_.23, v_res, v_x, v_y)) :|: v_.0 <= 0 eval_foo_bb1_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.0, v_.01, v_.2, v_.23, v_res, v_x, v_y)) :|: v_.01 <= 0 eval_foo_bb2_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y)) :|: TRUE eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y)) :|: v_.1 > 0 eval_foo_bb3_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb7_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y)) :|: v_.1 <= 0 eval_foo_bb4_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.1, v_.12, v_.1, v_.12 + 1, v_res, v_x, v_y)) :|: TRUE eval_foo_bb5_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb6_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y)) :|: v_.2 > 0 && v_.23 > 0 eval_foo_bb5_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.2, v_.23, v_.2, v_.23, v_res, v_x, v_y)) :|: v_.2 <= 0 eval_foo_bb5_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.2, v_.23, v_.2, v_.23, v_res, v_x, v_y)) :|: v_.23 <= 0 eval_foo_bb6_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.1, v_.12, v_.2 - 1, v_.23 - 1, v_res, v_x, v_y)) :|: TRUE eval_foo_bb7_in(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.1, v_.12, v_.2, v_.23, v_res, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_9] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 16*ar_1 + 3*ar_3 + 26) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_6 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 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) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_6 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 3 Pol(evalfoobb0in) = 3 Pol(evalfoobb1in) = 3 Pol(evalfoobb2in) = 3 Pol(evalfoobb3in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoobb7in) = 1 Pol(evalfoobb5in) = 2 Pol(evalfoobb6in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 3 orients all transitions weakly and the transitions evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_4 ] evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_2 ] evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= 1 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_6 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = V_2 Pol(evalfoobb0in) = V_2 Pol(evalfoobb1in) = V_1 Pol(evalfoobb2in) = V_1 - 1 Pol(evalfoobb3in) = V_5 Pol(evalfoobb4in) = V_5 Pol(evalfoobb7in) = V_5 Pol(evalfoobb5in) = V_7 Pol(evalfoobb6in) = V_7 - 1 Pol(evalfoostop) = V_5 Pol(koat_start) = V_2 orients all transitions weakly and the transitions evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= 1 /\ ar_7 >= 1 ] evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= 1 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_6 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ 0 >= ar_2 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= 1 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_6 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ 0 >= ar_7 ] (Comp: ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol evalfoobb1in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb2in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb3in: X_2 - X_5 >= 0 /\ X_1 - X_5 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb4in: X_2 - X_5 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_2 + X_5 - 2 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb5in: X_6 - X_8 + 1 >= 0 /\ X_5 - X_7 >= 0 /\ X_2 - X_7 >= 0 /\ X_1 - X_7 >= 0 /\ X_2 - X_5 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_2 + X_5 - 2 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb6in: X_6 - X_8 + 1 >= 0 /\ X_8 - 1 >= 0 /\ X_7 + X_8 - 2 >= 0 /\ X_6 + X_8 - 1 >= 0 /\ X_5 + X_8 - 2 >= 0 /\ X_2 + X_8 - 2 >= 0 /\ X_1 + X_8 - 2 >= 0 /\ X_5 - X_7 >= 0 /\ X_2 - X_7 >= 0 /\ X_1 - X_7 >= 0 /\ X_7 - 1 >= 0 /\ X_6 + X_7 - 1 >= 0 /\ X_5 + X_7 - 2 >= 0 /\ X_2 + X_7 - 2 >= 0 /\ X_1 + X_7 - 2 >= 0 /\ X_6 >= 0 /\ X_5 + X_6 - 1 >= 0 /\ X_2 + X_6 - 1 >= 0 /\ X_1 + X_6 - 1 >= 0 /\ X_2 - X_5 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_2 + X_5 - 2 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb7in: -X_5 >= 0 /\ X_2 - X_5 >= 0 /\ X_1 - X_5 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 ] (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 ] (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) start location: koat_start leaf cost: 0 By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] with all transitions in problem 7, the following new transition is obtained: koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] We thus obtain the following problem: 8: T: (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 ] (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 8: evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) We thus obtain the following problem: 9: T: (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 ] (Comp: ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 ] with all transitions in problem 9, the following new transition is obtained: evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 ] We thus obtain the following problem: 10: T: (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 ] (Comp: ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 ] with all transitions in problem 10, the following new transition is obtained: evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] We thus obtain the following problem: 11: T: (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 ] with all transitions in problem 11, the following new transition is obtained: evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] We thus obtain the following problem: 12: T: (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 12: evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] We thus obtain the following problem: 13: T: (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 ] with all transitions in problem 13, the following new transition is obtained: evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] We thus obtain the following problem: 14: T: (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 14: evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] We thus obtain the following problem: 15: T: (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 ] with all transitions in problem 15, the following new transition is obtained: evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] We thus obtain the following problem: 16: T: (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: 3, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 16: evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_4 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] We thus obtain the following problem: 17: T: (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ] with all transitions in problem 17, the following new transition is obtained: evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] We thus obtain the following problem: 18: T: (Comp: ar_1, Cost: 2) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 18: evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 ] We thus obtain the following problem: 19: T: (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ] with all transitions in problem 19, the following new transition is obtained: evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ ar_1 - ar_0 >= 0 /\ 0 >= 0 /\ -ar_0 >= 0 ] We thus obtain the following problem: 20: T: (Comp: 3, Cost: 3) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ ar_1 - ar_0 >= 0 /\ 0 >= 0 /\ -ar_0 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] with all transitions in problem 20, the following new transition is obtained: koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] We thus obtain the following problem: 21: T: (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] (Comp: 3, Cost: 3) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ ar_1 - ar_0 >= 0 /\ 0 >= 0 /\ -ar_0 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 21: evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) We thus obtain the following problem: 22: T: (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 3) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ ar_1 - ar_0 >= 0 /\ 0 >= 0 /\ -ar_0 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 ] with all transitions in problem 22, the following new transitions are obtained: evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7 + 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ ar_6 >= 1 /\ ar_6 - 1 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 ] We thus obtain the following problem: 23: T: (Comp: ?, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ?, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7 + 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ ar_6 >= 1 /\ ar_6 - 1 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 3) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ ar_1 - ar_0 >= 0 /\ 0 >= 0 /\ -ar_0 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 23 produces the following problem: 24: T: (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ?, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7 + 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ ar_6 >= 1 /\ ar_6 - 1 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 3) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ ar_1 - ar_0 >= 0 /\ 0 >= 0 /\ -ar_0 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb5in) = V_1 + V_7 - V_8 Pol(evalfoostop) = V_1 + V_5 - V_6 Pol(evalfoobb3in) = V_1 + V_2 - V_6 Pol(evalfoobb1in) = V_1 + V_2 - V_3 Pol(koat_start) = 2*V_2 - V_4 orients all transitions weakly and the transition evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7 + 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ ar_6 >= 1 /\ ar_6 - 1 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 ] strictly and produces the following problem: 25: T: (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: 2*ar_1 + ar_3, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7 + 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_7 /\ ar_6 >= 1 /\ ar_6 - 1 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 ] (Comp: ar_1, Cost: 3) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_6 /\ -ar_6 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7 - 1)) [ ar_5 - ar_7 + 1 >= 0 /\ ar_4 - ar_6 >= 0 /\ ar_1 - ar_6 >= 0 /\ ar_0 - ar_6 >= 0 /\ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_6 >= 1 /\ ar_7 >= 1 /\ ar_7 - 1 >= 0 /\ ar_6 + ar_7 - 2 >= 0 /\ ar_5 + ar_7 - 1 >= 0 /\ ar_4 + ar_7 - 2 >= 0 /\ ar_1 + ar_7 - 2 >= 0 /\ ar_0 + ar_7 - 2 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 1 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 2 >= 0 /\ ar_0 + ar_6 - 2 >= 0 /\ ar_5 >= 0 /\ ar_4 + ar_5 - 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 - 1 >= 0 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_4 /\ -ar_4 >= 0 ] (Comp: 3, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4, ar_5 + 1)) [ ar_1 - ar_4 >= 0 /\ ar_0 - ar_4 >= 0 /\ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= 1 /\ ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 3) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 /\ ar_1 - ar_0 >= 0 /\ 0 >= 0 /\ -ar_0 >= 0 ] (Comp: ar_1, Cost: 2) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2, ar_6, ar_7)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 16*ar_1 + 3*ar_3 + 26 Time: 2.138 sec (SMT: 1.440 sec) ---------------------------------------- (2) BOUNDS(1, n^1)