/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 378 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_a, v_b, v_x, v_y)) :|: v_a >= v_b && v_a <= v_b eval_foo_bb0_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_a < v_b eval_foo_bb0_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_a > v_b eval_foo_bb1_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_.0 >= 0 eval_foo_bb1_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_.01 >= 0 eval_foo_bb1_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: v_.0 < 0 && v_.01 < 0 eval_foo_bb2_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + v_a - v_b - 1, v_.01 + v_b - v_a - 1, v_a, v_b, v_x, v_y)) :|: TRUE eval_foo_bb3_in(v_.0, v_.01, v_a, v_b, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_a, v_b, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 4*Ar_3 + 2*Ar_3*Ar_5 + 2*Ar_5^2 + 10*Ar_5 + 18) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb3in) = 1 Pol(evalfoobb2in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfoobb1in: X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb2in: X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb2in) = V_5 Pol(evalfoobb1in) = V_5 + 1 and size complexities S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-2) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-4) = Ar_5 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-5) = Ar_5 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-5) = Ar_5 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-5) = Ar_5 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-5) = Ar_5 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-5) = Ar_5 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-5) = Ar_5 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-2) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-3) = Ar_3 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-4) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-5) = Ar_5 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 orients the transitions evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] weakly and the transition evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: Ar_5 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) 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) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] with all transitions in problem 5, the following new transition is obtained: koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] We thus obtain the following problem: 6: T: (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: Ar_5 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 6: evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) We thus obtain the following problem: 7: T: (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] (Comp: Ar_5 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] with all transitions in problem 7, the following new transition is obtained: evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] We thus obtain the following problem: 8: T: (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: Ar_5 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 8 produces the following problem: 9: T: (Comp: ?, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] (Comp: Ar_5 + 1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: Ar_5 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb1in) = V_3 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ]", 0-5) = Ar_5 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ]", 0-5) = Ar_5 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-2) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-4) = Ar_5 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ]", 0-5) = Ar_5 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 + Ar_3 + Ar_5 + 2 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-2) = Ar_3 + Ar_5 + 2 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_2 + 1 /\\ 0 >= Ar_4 + 1 ]", 0-5) = Ar_5 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-2) = Ar_3 + Ar_5 + 2 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_4 >= 0 ]", 0-5) = Ar_5 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-2) = Ar_3 + Ar_5 + 2 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-3) = Ar_3 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-4) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-5) = Ar_5 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-2) = Ar_3 + Ar_5 + 2 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 >= 0 ]", 0-5) = Ar_5 orients the transitions evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] weakly and the transition evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] strictly and produces the following problem: 10: T: (Comp: 2*Ar_3 + Ar_3*Ar_5 + Ar_5^2 + 4*Ar_5 + 4, Cost: 2) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= 0 ] (Comp: Ar_5 + 1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + Ar_0 - Ar_1 - 1, Ar_3, Ar_4 + Ar_1 - Ar_0 - 1, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: Ar_5 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 + 1 /\ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) [ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_3 + 2*Ar_3*Ar_5 + 2*Ar_5^2 + 10*Ar_5 + 18 Time: 0.404 sec (SMT: 0.312 sec) ---------------------------------------- (2) BOUNDS(1, n^2)