/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^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 584 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: TRUE eval_foo_bb0_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: TRUE eval_foo_bb1_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: v_.01 > v_z eval_foo_bb1_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: v_.02 > v_z eval_foo_bb1_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb6_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: v_.01 <= v_z && v_.02 <= v_z eval_foo_bb2_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: v_.01 > v_z eval_foo_bb2_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb4_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: v_.01 <= v_z eval_foo_bb3_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01 - 1, v_.02, v_c, v_x, v_y, v_z)) :|: TRUE eval_foo_bb4_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02 - 1, v_c, v_x, v_y, v_z)) :|: v_.02 > v_z eval_foo_bb4_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.01, v_.02, v_c, v_x, v_y, v_z)) :|: v_.02 <= v_z eval_foo_bb5_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.1, v_.2, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: TRUE eval_foo_bb6_in(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z) -> Com_1(eval_foo_stop(v_.01, v_.02, v_.1, v_.2, v_c, v_x, v_y, v_z)) :|: TRUE The start-symbols are:[eval_foo_start_8] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 8*Ar_1 + 14*Ar_4 + 6*Ar_3 + 11) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb2in) = 2 Pol(evalfoobb6in) = 1 Pol(evalfoobb3in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoobb5in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = V_2 - V_5 Pol(evalfoobb0in) = V_2 - V_5 Pol(evalfoobb1in) = V_1 - V_5 Pol(evalfoobb2in) = V_1 - V_5 Pol(evalfoobb6in) = V_1 - V_5 Pol(evalfoobb3in) = V_1 - V_5 - 1 Pol(evalfoobb4in) = V_1 - V_5 Pol(evalfoobb5in) = -V_5 + V_6 Pol(evalfoostop) = V_1 - V_5 Pol(koat_start) = V_2 - V_5 orients all transitions weakly and the transition evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = V_4 - V_5 Pol(evalfoobb0in) = V_4 - V_5 Pol(evalfoobb1in) = V_3 - V_5 Pol(evalfoobb2in) = V_3 - V_5 Pol(evalfoobb6in) = V_3 - V_5 Pol(evalfoobb3in) = V_3 - V_5 Pol(evalfoobb4in) = V_3 - V_5 Pol(evalfoobb5in) = -V_5 + V_7 Pol(evalfoostop) = V_3 - V_5 Pol(koat_start) = V_4 - V_5 orients all transitions weakly and the transition evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ Ar_2 >= Ar_4 + 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) (Comp: Ar_3 + Ar_4, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol evalfoobb1in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb2in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb3in: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb4in: -X_1 + X_5 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb5in: X_4 - X_7 >= 0 /\ X_3 - X_7 >= 0 /\ -X_3 + X_7 + 1 >= 0 /\ X_2 - X_6 >= 0 /\ X_1 - X_6 >= 0 /\ -X_1 + X_6 + 1 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb6in: -X_3 + X_5 >= 0 /\ -X_1 + X_5 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 This yielded 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) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_3 - Ar_6 >= 0 /\ Ar_2 - Ar_6 >= 0 /\ -Ar_2 + Ar_6 + 1 >= 0 /\ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_5 >= 0 /\ -Ar_0 + Ar_5 + 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: Ar_3 + Ar_4, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) 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) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_3 - Ar_6 >= 0 /\ Ar_2 - Ar_6 >= 0 /\ -Ar_2 + Ar_6 + 1 >= 0 /\ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_5 >= 0 /\ -Ar_0 + Ar_5 + 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: Ar_3 + Ar_4, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) We thus obtain the following problem: 9: T: (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_3 - Ar_6 >= 0 /\ Ar_2 - Ar_6 >= 0 /\ -Ar_2 + Ar_6 + 1 >= 0 /\ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_5 >= 0 /\ -Ar_0 + Ar_5 + 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: Ar_3 + Ar_4, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 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) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] with all transitions in problem 9, the following new transition is obtained: evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 + 1 >= 0 ] We thus obtain the following problem: 10: T: (Comp: Ar_1 + Ar_4, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 + 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_3 - Ar_6 >= 0 /\ Ar_2 - Ar_6 >= 0 /\ -Ar_2 + Ar_6 + 1 >= 0 /\ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_5 >= 0 /\ -Ar_0 + Ar_5 + 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: Ar_3 + Ar_4, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] with all transitions in problem 10, the following new transition is obtained: evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 /\ Ar_3 - Ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ Ar_1 - Ar_0 >= 0 ] We thus obtain the following problem: 11: T: (Comp: Ar_3 + Ar_4, Cost: 2) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 /\ Ar_3 - Ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ Ar_1 - Ar_0 >= 0 ] (Comp: Ar_1 + Ar_4, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 + 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_3 - Ar_6 >= 0 /\ Ar_2 - Ar_6 >= 0 /\ -Ar_2 + Ar_6 + 1 >= 0 /\ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_5 >= 0 /\ -Ar_0 + Ar_5 + 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 ] with all transitions in problem 11, the following new transition is obtained: evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 >= 0 ] We thus obtain the following problem: 12: T: (Comp: ?, Cost: 2) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 >= 0 ] (Comp: Ar_3 + Ar_4, Cost: 2) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 /\ Ar_3 - Ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ Ar_1 - Ar_0 >= 0 ] (Comp: Ar_1 + Ar_4, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 + 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_3 - Ar_6 >= 0 /\ Ar_2 - Ar_6 >= 0 /\ -Ar_2 + Ar_6 + 1 >= 0 /\ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_5 >= 0 /\ -Ar_0 + Ar_5 + 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 12: evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_5, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_3 - Ar_6 >= 0 /\ Ar_2 - Ar_6 >= 0 /\ -Ar_2 + Ar_6 + 1 >= 0 /\ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_5 >= 0 /\ -Ar_0 + Ar_5 + 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] We thus obtain the following problem: 13: T: (Comp: Ar_1 + Ar_4, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 + 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 >= 0 ] (Comp: Ar_3 + Ar_4, Cost: 2) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 /\ Ar_3 - Ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ Ar_1 - Ar_0 >= 0 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 13 produces the following problem: 14: T: (Comp: Ar_1 + Ar_4, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0 - 1, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 + 1 >= 0 ] (Comp: Ar_3 + 2*Ar_4 + Ar_1 + 1, Cost: 2) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_0, Ar_2)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_2 /\ Ar_3 - Ar_2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_1 - Ar_0 >= 0 ] (Comp: Ar_3 + Ar_4, Cost: 2) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4, Ar_0, Ar_2 - 1)) [ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 /\ Ar_3 - Ar_2 + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ Ar_1 - Ar_0 >= 0 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: Ar_3 + 2*Ar_4 + Ar_1 + 1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: Ar_1 + Ar_4 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_4 + 1 ] (Comp: Ar_3 + 2*Ar_4 + Ar_1 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_2 + Ar_3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_4 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 8*Ar_1 + 14*Ar_4 + 6*Ar_3 + 11 Time: 0.630 sec (SMT: 0.442 sec) ---------------------------------------- (2) BOUNDS(1, n^1)