2.93/2.08 WORST_CASE(?, O(n^1)) 2.93/2.09 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.93/2.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.93/2.09 2.93/2.09 2.93/2.09 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.93/2.09 2.93/2.09 (0) CpxIntTrs 2.93/2.09 (1) Koat Proof [FINISHED, 799 ms] 2.93/2.09 (2) BOUNDS(1, n^1) 2.93/2.09 2.93/2.09 2.93/2.09 ---------------------------------------- 2.93/2.09 2.93/2.09 (0) 2.93/2.09 Obligation: 2.93/2.09 Complexity Int TRS consisting of the following rules: 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 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 2.93/2.09 2.93/2.09 The start-symbols are:[eval_foo_start_8] 2.93/2.09 2.93/2.09 2.93/2.09 ---------------------------------------- 2.93/2.09 2.93/2.09 (1) Koat Proof (FINISHED) 2.93/2.09 YES(?, 8*ar_1 + 14*ar_4 + 6*ar_3 + 11) 2.93/2.09 2.93/2.09 2.93/2.09 2.93/2.09 Initial complexity problem: 2.93/2.09 2.93/2.09 1: T: 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 start location: koat_start 2.93/2.09 2.93/2.09 leaf cost: 0 2.93/2.09 2.93/2.09 2.93/2.09 2.93/2.09 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.93/2.09 2.93/2.09 2: T: 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 start location: koat_start 2.93/2.09 2.93/2.09 leaf cost: 0 2.93/2.09 2.93/2.09 2.93/2.09 2.93/2.09 A polynomial rank function with 2.93/2.09 2.93/2.09 Pol(evalfoostart) = 2 2.93/2.09 2.93/2.09 Pol(evalfoobb0in) = 2 2.93/2.09 2.93/2.09 Pol(evalfoobb1in) = 2 2.93/2.09 2.93/2.09 Pol(evalfoobb2in) = 2 2.93/2.09 2.93/2.09 Pol(evalfoobb6in) = 1 2.93/2.09 2.93/2.09 Pol(evalfoobb3in) = 2 2.93/2.09 2.93/2.09 Pol(evalfoobb4in) = 2 2.93/2.09 2.93/2.09 Pol(evalfoobb5in) = 2 2.93/2.09 2.93/2.09 Pol(evalfoostop) = 0 2.93/2.09 2.93/2.09 Pol(koat_start) = 2 2.93/2.09 2.93/2.09 orients all transitions weakly and the transitions 2.93/2.09 2.93/2.09 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)) 2.93/2.09 2.93/2.09 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 ] 2.93/2.09 2.93/2.09 strictly and produces the following problem: 2.93/2.09 2.93/2.09 3: T: 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 start location: koat_start 2.93/2.09 2.93/2.09 leaf cost: 0 2.93/2.09 2.93/2.09 2.93/2.09 2.93/2.09 A polynomial rank function with 2.93/2.09 2.93/2.09 Pol(evalfoostart) = V_2 - V_5 2.93/2.09 2.93/2.09 Pol(evalfoobb0in) = V_2 - V_5 2.93/2.09 2.93/2.09 Pol(evalfoobb1in) = V_1 - V_5 2.93/2.09 2.93/2.09 Pol(evalfoobb2in) = V_1 - V_5 2.93/2.09 2.93/2.09 Pol(evalfoobb6in) = V_1 - V_5 2.93/2.09 2.93/2.09 Pol(evalfoobb3in) = V_1 - V_5 - 1 2.93/2.09 2.93/2.09 Pol(evalfoobb4in) = V_1 - V_5 2.93/2.09 2.93/2.09 Pol(evalfoobb5in) = -V_5 + V_6 2.93/2.09 2.93/2.09 Pol(evalfoostop) = V_1 - V_5 2.93/2.09 2.93/2.09 Pol(koat_start) = V_2 - V_5 2.93/2.09 2.93/2.09 orients all transitions weakly and the transition 2.93/2.09 2.93/2.09 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 ] 2.93/2.09 2.93/2.09 strictly and produces the following problem: 2.93/2.09 2.93/2.09 4: T: 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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)) 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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 ] 2.93/2.09 2.93/2.09 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 Repeatedly propagating knowledge in problem 4 produces the following problem: 2.93/2.10 2.93/2.10 5: T: 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 A polynomial rank function with 2.93/2.10 2.93/2.10 Pol(evalfoostart) = V_4 - V_5 2.93/2.10 2.93/2.10 Pol(evalfoobb0in) = V_4 - V_5 2.93/2.10 2.93/2.10 Pol(evalfoobb1in) = V_3 - V_5 2.93/2.10 2.93/2.10 Pol(evalfoobb2in) = V_3 - V_5 2.93/2.10 2.93/2.10 Pol(evalfoobb6in) = V_3 - V_5 2.93/2.10 2.93/2.10 Pol(evalfoobb3in) = V_3 - V_5 2.93/2.10 2.93/2.10 Pol(evalfoobb4in) = V_3 - V_5 2.93/2.10 2.93/2.10 Pol(evalfoobb5in) = -V_5 + V_7 2.93/2.10 2.93/2.10 Pol(evalfoostop) = V_3 - V_5 2.93/2.10 2.93/2.10 Pol(koat_start) = V_4 - V_5 2.93/2.10 2.93/2.10 orients all transitions weakly and the transition 2.93/2.10 2.93/2.10 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 ] 2.93/2.10 2.93/2.10 strictly and produces the following problem: 2.93/2.10 2.93/2.10 6: T: 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 Applied AI with 'oct' on problem 6 to obtain the following invariants: 2.93/2.10 2.93/2.10 For symbol evalfoobb1in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 2.93/2.10 2.93/2.10 For symbol evalfoobb2in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 2.93/2.10 2.93/2.10 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 2.93/2.10 2.93/2.10 For symbol evalfoobb4in: -X_1 + X_5 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 2.93/2.10 2.93/2.10 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 2.93/2.10 2.93/2.10 For symbol evalfoobb6in: -X_3 + X_5 >= 0 /\ -X_1 + X_5 >= 0 /\ -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 This yielded the following problem: 2.93/2.10 2.93/2.10 7: T: 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 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: 2.93/2.10 2.93/2.10 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 ] 2.93/2.10 2.93/2.10 We thus obtain the following problem: 2.93/2.10 2.93/2.10 8: T: 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 Testing for reachability in the complexity graph removes the following transition from problem 8: 2.93/2.10 2.93/2.10 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)) 2.93/2.10 2.93/2.10 We thus obtain the following problem: 2.93/2.10 2.93/2.10 9: T: 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 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: 2.93/2.10 2.93/2.10 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 ] 2.93/2.10 2.93/2.10 We thus obtain the following problem: 2.93/2.10 2.93/2.10 10: T: 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 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: 2.93/2.10 2.93/2.10 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 ] 2.93/2.10 2.93/2.10 We thus obtain the following problem: 2.93/2.10 2.93/2.10 11: T: 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 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: 2.93/2.10 2.93/2.10 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 ] 2.93/2.10 2.93/2.10 We thus obtain the following problem: 2.93/2.10 2.93/2.10 12: T: 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 Testing for reachability in the complexity graph removes the following transition from problem 12: 2.93/2.10 2.93/2.10 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 ] 2.93/2.10 2.93/2.10 We thus obtain the following problem: 2.93/2.10 2.93/2.10 13: T: 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 Repeatedly propagating knowledge in problem 13 produces the following problem: 2.93/2.10 2.93/2.10 14: T: 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 (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)) 2.93/2.10 2.93/2.10 (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 ] 2.93/2.10 2.93/2.10 start location: koat_start 2.93/2.10 2.93/2.10 leaf cost: 0 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 Complexity upper bound 8*ar_1 + 14*ar_4 + 6*ar_3 + 11 2.93/2.10 2.93/2.10 2.93/2.10 2.93/2.10 Time: 0.809 sec (SMT: 0.584 sec) 2.93/2.10 2.93/2.10 2.93/2.10 ---------------------------------------- 2.93/2.10 2.93/2.10 (2) 2.93/2.10 BOUNDS(1, n^1) 3.00/2.12 EOF