/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^3)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). (0) CpxIntTrs (1) Koat Proof [FINISHED, 1087 ms] (2) BOUNDS(1, n^3) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE eval_foo_bb0_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_z, v_y, v_x, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE eval_foo_bb1_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: v_.04 >= v_.02 eval_foo_bb1_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: v_.04 < v_.02 eval_foo_bb2_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: v_.01 > 1 eval_foo_bb2_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb4_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: v_.01 <= 1 eval_foo_bb3_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.01 - 1, v_.02, v_.04 + v_.01 - 1, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE eval_foo_bb4_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.01, v_.02 + 1, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE eval_foo_bb5_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_stop(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE The start-symbols are:[eval_foo_start_10] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 3*ar_1*ar_3 + 9*ar_1^2 + 3*ar_1*ar_5 + 3*ar_1^3 + 6*ar_3 + 12*ar_1 + 6*ar_5 + 20) 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_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(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 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalfoobb5in(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_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(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 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalfoobb5in(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(evalfoobb2in) = 2 Pol(evalfoobb5in) = 1 Pol(evalfoobb3in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb5in(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(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 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_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(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 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) (Comp: 2, Cost: 1) evalfoobb5in(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) = V_2 + 1 Pol(evalfoobb0in) = V_2 + 1 Pol(evalfoobb1in) = V_1 + 1 Pol(evalfoobb2in) = V_1 + 1 Pol(evalfoobb5in) = V_1 Pol(evalfoobb3in) = V_1 Pol(evalfoobb4in) = V_1 + 1 Pol(evalfoostop) = V_1 Pol(koat_start) = V_2 + 1 orients all transitions weakly and the transition evalfoobb2in(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 >= 2 ] 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) -> 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_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb2in(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 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) (Comp: 2, Cost: 1) evalfoobb5in(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 4 produces the following problem: 5: 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_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb2in(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 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) (Comp: 2, Cost: 1) evalfoobb5in(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 5 to obtain the following invariants: For symbol evalfoobb1in: X_5 - X_6 >= 0 /\ X_3 - X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb2in: X_5 - X_6 >= 0 /\ -X_4 + X_5 >= 0 /\ -X_3 + X_5 >= 0 /\ X_3 - X_4 >= 0 /\ -X_1 + X_2 >= 0 For symbol evalfoobb3in: X_5 - X_6 >= 0 /\ -X_4 + X_5 >= 0 /\ -X_3 + X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalfoobb4in: X_5 - X_6 >= 0 /\ -X_4 + X_5 >= 0 /\ -X_3 + X_5 >= 0 /\ X_3 - X_4 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 + 1 >= 0 For symbol evalfoobb5in: X_5 - X_6 >= 0 /\ X_3 - X_6 - 1 >= 0 /\ X_3 - X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ -X_1 + X_2 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 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) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb2in(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_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 6, 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: 7: 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) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 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) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb2in(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_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 7: 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: 8: T: (Comp: ar_1 + 1, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb2in(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_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] (Comp: 2, Cost: 1) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] with all transitions in problem 8, the following new transition is obtained: evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] We thus obtain the following problem: 9: T: (Comp: ar_1 + 1, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 1) evalfoobb2in(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_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] (Comp: 2, Cost: 1) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 evalfoobb2in(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_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] with all transitions in problem 9, the following new transition is obtained: evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] We thus obtain the following problem: 10: T: (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: ar_1 + 1, Cost: 2) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] (Comp: 2, Cost: 1) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 Testing for reachability in the complexity graph removes the following transition from problem 10: evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] We thus obtain the following problem: 11: T: (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] (Comp: 2, Cost: 1) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] with all transitions in problem 11, the following new transition is obtained: evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 ] We thus obtain the following problem: 12: T: (Comp: ?, Cost: 2) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 Testing for reachability in the complexity graph removes the following transition from problem 12: evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] We thus obtain the following problem: 13: T: (Comp: ?, Cost: 2) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 ] with all transitions in problem 13, the following new transition is obtained: evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 0 ] We thus obtain the following problem: 14: T: (Comp: 2, Cost: 2) evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 0 ] (Comp: ?, Cost: 2) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 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) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 Testing for reachability in the complexity graph removes the following transition from problem 14: evalfoobb5in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ] We thus obtain the following problem: 15: T: (Comp: ?, Cost: 2) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 2) evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 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_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (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 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 ] with all transitions in problem 15, the following new transition is obtained: koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ] We thus obtain the following problem: 16: T: (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ] (Comp: ?, Cost: 2) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 2) evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 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_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 16: evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) We thus obtain the following problem: 17: T: (Comp: ?, Cost: 2) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 2) evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 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_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 ] with all transitions in problem 17, the following new transitions are obtained: evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_2 + 1 >= ar_4 + 1 /\ ar_2 - ar_5 >= 0 /\ ar_2 - ar_4 >= 0 ] evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_4 >= ar_2 + 1 ] We thus obtain the following problem: 18: T: (Comp: ?, Cost: 4) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_2 + 1 >= ar_4 + 1 /\ ar_2 - ar_5 >= 0 /\ ar_2 - ar_4 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_4 >= ar_2 + 1 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 2) evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 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_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 18 produces the following problem: 19: T: (Comp: ?, Cost: 4) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_2 + 1 >= ar_4 + 1 /\ ar_2 - ar_5 >= 0 /\ ar_2 - ar_4 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_4 >= ar_2 + 1 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 2) evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 0 ] (Comp: 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_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb2in) = 1 Pol(evalfoostop) = 0 Pol(evalfoobb1in) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_2 + 1 >= ar_4 + 1 /\ ar_2 - ar_5 >= 0 /\ ar_2 - ar_4 >= 0 ] strictly and produces the following problem: 20: T: (Comp: 1, Cost: 4) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_2 + 1 >= ar_4 + 1 /\ ar_2 - ar_5 >= 0 /\ ar_2 - ar_4 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_4 >= ar_2 + 1 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 2) evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 0 ] (Comp: 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_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb2in) = -V_3 + V_5 + 1 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ]", 0-0) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, 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(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ]", 0-2) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, 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(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ]", 0-4) = ar_5 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 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_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_4 >= ar_2 ]", 0-0) = 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_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_4 >= ar_2 ]", 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_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_4 >= ar_2 ]", 0-2) = 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_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_4 >= ar_2 ]", 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_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_4 >= ar_2 ]", 0-4) = 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_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_4 >= ar_2 ]", 0-5) = ar_5 S("evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_2 >= ar_4 + 1 /\\ ar_2 - ar_5 - 1 >= 0 /\\ ar_2 - ar_4 - 1 >= 0 ]", 0-0) = ar_1 S("evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_2 >= ar_4 + 1 /\\ ar_2 - ar_5 - 1 >= 0 /\\ ar_2 - ar_4 - 1 >= 0 ]", 0-1) = ar_1 S("evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_2 >= ar_4 + 1 /\\ ar_2 - ar_5 - 1 >= 0 /\\ ar_2 - ar_4 - 1 >= 0 ]", 0-2) = ar_3 S("evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_2 >= ar_4 + 1 /\\ ar_2 - ar_5 - 1 >= 0 /\\ ar_2 - ar_4 - 1 >= 0 ]", 0-3) = ar_3 S("evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_2 >= ar_4 + 1 /\\ ar_2 - ar_5 - 1 >= 0 /\\ ar_2 - ar_4 - 1 >= 0 ]", 0-4) = ar_5 S("evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_2 >= ar_4 + 1 /\\ ar_2 - ar_5 - 1 >= 0 /\\ ar_2 - ar_4 - 1 >= 0 ]", 0-5) = ar_5 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 2 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ ar_4 + ar_0 - 1 >= ar_2 ]", 0-0) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 2 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ ar_4 + ar_0 - 1 >= ar_2 ]", 0-1) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 2 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ ar_4 + ar_0 - 1 >= ar_2 ]", 0-2) = ar_3 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 2 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ ar_4 + ar_0 - 1 >= ar_2 ]", 0-3) = ar_3 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 2 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ ar_4 + ar_0 - 1 >= ar_2 ]", 0-4) = 2*ar_1 + ar_5 + ar_1^2 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 2 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\\ -ar_0 + ar_1 + 1 >= 0 /\\ ar_4 + ar_0 - 1 >= ar_2 ]", 0-5) = ar_5 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_4 >= ar_2 + 1 ]", 0-0) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_4 >= ar_2 + 1 ]", 0-1) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_4 >= ar_2 + 1 ]", 0-2) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_4 >= ar_2 + 1 ]", 0-3) = ar_3 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_4 >= ar_2 + 1 ]", 0-4) = ar_5 + 2*ar_1 + ar_1^2 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_4 >= ar_2 + 1 ]", 0-5) = ar_5 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_2 + 1 >= ar_4 + 1 /\\ ar_2 - ar_5 >= 0 /\\ ar_2 - ar_4 >= 0 ]", 0-0) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_2 + 1 >= ar_4 + 1 /\\ ar_2 - ar_5 >= 0 /\\ ar_2 - ar_4 >= 0 ]", 0-1) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_2 + 1 >= ar_4 + 1 /\\ ar_2 - ar_5 >= 0 /\\ ar_2 - ar_4 >= 0 ]", 0-2) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_2 + 1 >= ar_4 + 1 /\\ ar_2 - ar_5 >= 0 /\\ ar_2 - ar_4 >= 0 ]", 0-3) = ar_3 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_2 + 1 >= ar_4 + 1 /\\ ar_2 - ar_5 >= 0 /\\ ar_2 - ar_4 >= 0 ]", 0-4) = ar_5 + 2*ar_1 + ar_1^2 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\\ -ar_3 + ar_4 >= 0 /\\ -ar_2 + ar_4 >= 0 /\\ ar_2 - ar_3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 1 >= ar_0 /\\ -ar_0 + 1 >= 0 /\\ ar_2 - ar_3 + 1 >= 0 /\\ ar_2 + 1 >= ar_4 + 1 /\\ ar_2 - ar_5 >= 0 /\\ ar_2 - ar_4 >= 0 ]", 0-5) = ar_5 orients the transitions evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_4 >= ar_2 + 1 ] weakly and the transition evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_4 >= ar_2 + 1 ] strictly and produces the following problem: 21: T: (Comp: 1, Cost: 4) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_2 + 1 >= ar_4 + 1 /\ ar_2 - ar_5 >= 0 /\ ar_2 - ar_4 >= 0 ] (Comp: ar_1*ar_3 + 3*ar_1^2 + ar_1*ar_5 + ar_1^3 + 2*ar_3 + 3*ar_1 + 2*ar_5 + 2, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 /\ -ar_0 + 1 >= 0 /\ ar_2 - ar_3 + 1 >= 0 /\ ar_4 >= ar_2 + 1 ] (Comp: ar_1 + 1, Cost: 3) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) [ ar_4 - ar_5 >= 0 /\ -ar_3 + ar_4 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 + ar_0 - ar_5 - 1 >= 0 /\ -ar_0 + ar_1 + 1 >= 0 /\ ar_4 + ar_0 - 1 >= ar_2 ] (Comp: 2, Cost: 2) evalfoobb1in(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)) [ ar_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_2 >= ar_4 + 1 /\ ar_2 - ar_5 - 1 >= 0 /\ ar_2 - ar_4 - 1 >= 0 ] (Comp: 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_4 - ar_5 >= 0 /\ ar_2 - ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_4 >= ar_2 ] (Comp: 1, Cost: 2) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 3*ar_1*ar_3 + 9*ar_1^2 + 3*ar_1*ar_5 + 3*ar_1^3 + 6*ar_3 + 12*ar_1 + 6*ar_5 + 20 Time: 1.047 sec (SMT: 0.844 sec) ---------------------------------------- (2) BOUNDS(1, n^3)