/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 485 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_render_ht_start(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb0_in(v_.0, v_0, v_level, v_old_level)) :|: TRUE eval_render_ht_bb0_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb1_in(v_old_level, v_0, v_level, v_old_level)) :|: TRUE eval_render_ht_bb1_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_LeafBlock_in(v_.0, v_level - v_.0, v_level, v_old_level)) :|: TRUE eval_render_ht_LeafBlock_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb2_in(v_.0, v_0, v_level, v_old_level)) :|: v_0 + 7 <= 14 eval_render_ht_LeafBlock_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_NewDefault_in(v_.0, v_0, v_level, v_old_level)) :|: v_0 + 7 > 14 eval_render_ht_bb2_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_stop(v_.0, v_0, v_level, v_old_level)) :|: TRUE eval_render_ht_NewDefault_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb3_in(v_.0, v_0, v_level, v_old_level)) :|: TRUE eval_render_ht_bb3_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb1_in(v_.0 + 4, v_0, v_level, v_old_level)) :|: v_level > v_.0 eval_render_ht_bb3_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb1_in(v_.0 - 4, v_0, v_level, v_old_level)) :|: v_level <= v_.0 The start-symbols are:[eval_render_ht_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 6*ar_1 + 6*ar_3 + 11) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: ?, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ] (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 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) evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: ?, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ] (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrenderhtstart) = 2 Pol(evalrenderhtbb0in) = 2 Pol(evalrenderhtbb1in) = 2 Pol(evalrenderhtLeafBlockin) = 2 Pol(evalrenderhtbb2in) = 1 Pol(evalrenderhtNewDefaultin) = 2 Pol(evalrenderhtstop) = 0 Pol(evalrenderhtbb3in) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ] (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalrenderhtNewDefaultin: X_3 - 8 >= 0 For symbol evalrenderhtbb2in: -X_3 + 7 >= 0 For symbol evalrenderhtbb3in: X_3 - 8 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) start location: koat_start leaf cost: 0 By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained: koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] We thus obtain the following problem: 5: T: (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 5: evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) We thus obtain the following problem: 6: T: (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ] (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: ?, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] with all transitions in problem 6, the following new transition is obtained: evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] We thus obtain the following problem: 7: T: (Comp: ?, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ] (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: ?, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] with all transitions in problem 7, the following new transition is obtained: evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] We thus obtain the following problem: 8: T: (Comp: ?, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] (Comp: ?, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ] (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: ?, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 8 produces the following problem: 9: T: (Comp: ?, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] (Comp: ?, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ] (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: 1, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrenderhtNewDefaultin) = -V_1 + V_4 Pol(evalrenderhtbb3in) = -V_1 + V_4 Pol(evalrenderhtLeafBlockin) = -V_1 + V_4 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 S("evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1 S("evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))", 0-0) = ar_1 S("evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))", 0-1) = ar_1 S("evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))", 0-2) = ar_1 + ar_3 S("evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))", 0-3) = ar_3 S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]", 0-0) = ? S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]", 0-1) = ar_1 S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]", 0-2) = ? S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]", 0-3) = ar_3 S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]", 0-0) = ? S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]", 0-1) = ar_1 S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]", 0-2) = ? S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]", 0-3) = ar_3 S("evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]", 0-0) = ? S("evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]", 0-1) = ar_1 S("evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]", 0-2) = ? S("evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]", 0-3) = ar_3 S("evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]", 0-0) = ? S("evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]", 0-1) = ar_1 S("evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]", 0-2) = ? S("evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]", 0-3) = ar_3 S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ? S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ar_1 S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = ar_3 S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_0 >= ar_3 ]", 0-0) = ? S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_0 >= ar_3 ]", 0-1) = ar_1 S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_0 >= ar_3 ]", 0-2) = ? S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_0 >= ar_3 ]", 0-3) = ar_3 orients the transitions evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] weakly and the transition evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] strictly and produces the following problem: 10: T: (Comp: ?, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] (Comp: ar_1 + ar_3, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ] (Comp: ?, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ?, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: 1, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 10 produces the following problem: 11: T: (Comp: ar_1 + ar_3 + 1, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] (Comp: ar_1 + ar_3, Cost: 2) evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ] (Comp: ar_1 + ar_3 + 1, Cost: 1) evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ] (Comp: 2, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ] (Comp: ar_1 + ar_3 + 1, Cost: 1) evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ] (Comp: 1, Cost: 1) evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3)) (Comp: 1, Cost: 1) evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 6*ar_1 + 6*ar_3 + 11 Time: 0.441 sec (SMT: 0.371 sec) ---------------------------------------- (2) BOUNDS(1, n^1)