/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 369 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_complex_start(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb0_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: TRUE eval_complex_bb0_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb1_in(v_a, v_b, v_.1, v_.12, v_a, v_b)) :|: TRUE eval_complex_bb1_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.0, v_.01, v_a, v_b)) :|: v_.0 < 30 eval_complex_bb1_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb5_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.0 >= 30 eval_complex_bb2_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.12 < v_.1 eval_complex_bb2_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb4_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.12 >= v_.1 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 10, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 >= 10 && v_.12 + 7 <= 12 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 < 10 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 > 12 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 10, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 >= 10 && v_.12 + 2 <= 12 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 < 10 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 > 12 eval_complex_bb4_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb1_in(v_.1 + 2, v_.12 - 10, v_.1, v_.12, v_a, v_b)) :|: TRUE eval_complex_bb5_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_stop(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: TRUE The start-symbols are:[eval_complex_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 35*Ar_1 + 6*Ar_3 + 1200) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ] (Comp: ?, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ] (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 10, Ar_5 + 7)) [ Ar_5 >= 6 /\ Ar_5 >= 3 /\ 5 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 /\ 2 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 10, Ar_5 + 2)) [ 5 >= Ar_5 /\ Ar_5 >= 8 /\ 10 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ 7 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ Ar_5 >= 11 ] (Comp: ?, Cost: 1) evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(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(evalcomplexstart(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 transitions from problem 1: evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 10, Ar_5 + 7)) [ Ar_5 >= 6 /\ Ar_5 >= 3 /\ 5 >= Ar_5 ] evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 /\ 2 >= Ar_5 ] evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 10, Ar_5 + 2)) [ 5 >= Ar_5 /\ Ar_5 >= 8 /\ 10 >= Ar_5 ] evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ Ar_5 >= 11 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ 7 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ] (Comp: ?, Cost: 1) evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ] (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ] (Comp: ?, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ] (Comp: ?, Cost: 1) evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(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(evalcomplexstart(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 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ 7 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ] (Comp: ?, Cost: 1) evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ] (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ] (Comp: ?, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ] (Comp: 1, Cost: 1) evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(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(evalcomplexstart(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(evalcomplexbb4in) = 2 Pol(evalcomplexbb1in) = 2 Pol(evalcomplexbb3in) = 2 Pol(evalcomplexbb2in) = 2 Pol(evalcomplexbb5in) = 1 Pol(evalcomplexstop) = 0 Pol(evalcomplexbb0in) = 2 Pol(evalcomplexstart) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ 7 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ] (Comp: 2, Cost: 1) evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ] (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ] (Comp: 2, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ] (Comp: ?, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ] (Comp: 1, Cost: 1) evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(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(evalcomplexstart(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(evalcomplexbb4in) = -V_5 + 28 Pol(evalcomplexbb1in) = -V_1 + 30 Pol(evalcomplexbb3in) = -V_5 + 27 Pol(evalcomplexbb2in) = -V_5 + 28 Pol(evalcomplexbb5in) = -V_1 Pol(evalcomplexstop) = -V_1 Pol(evalcomplexbb0in) = -V_2 + 30 Pol(evalcomplexstart) = -V_2 + 30 Pol(koat_start) = -V_2 + 30 orients all transitions weakly and the transition evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ 7 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ] (Comp: 2, Cost: 1) evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ] (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ] (Comp: 2, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ] (Comp: Ar_1 + 30, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ] (Comp: 1, Cost: 1) evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(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(evalcomplexstart(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(evalcomplexbb4in) = 1 Pol(evalcomplexbb1in) = 0 Pol(evalcomplexbb3in) = 2 Pol(evalcomplexbb2in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ]", 0-0) = ? S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ]", 0-1) = Ar_1 S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ]", 0-2) = ? S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ]", 0-3) = Ar_3 S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ]", 0-4) = ? S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ]", 0-5) = ? S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ]", 0-0) = ? S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ]", 0-1) = Ar_1 S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ]", 0-2) = ? S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ]", 0-3) = Ar_3 S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ]", 0-4) = ? S("evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ]", 0-5) = ? S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ]", 0-0) = ? S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ]", 0-1) = Ar_1 S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ]", 0-2) = ? S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ]", 0-3) = Ar_3 S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ]", 0-4) = ? S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ]", 0-5) = ? S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ]", 0-0) = ? S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ]", 0-1) = Ar_1 S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ]", 0-2) = ? S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ]", 0-3) = Ar_3 S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ]", 0-4) = ? S("evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ]", 0-5) = ? S("evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = ? S("evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = ? S("evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ]", 0-0) = ? S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ]", 0-1) = Ar_1 S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ]", 0-2) = ? S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ]", 0-3) = Ar_3 S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ]", 0-4) = ? S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ]", 0-5) = ? S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\\ 7 >= Ar_5 ]", 0-0) = ? S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\\ 7 >= Ar_5 ]", 0-1) = Ar_1 S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\\ 7 >= Ar_5 ]", 0-2) = ? S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\\ 7 >= Ar_5 ]", 0-3) = Ar_3 S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\\ 7 >= Ar_5 ]", 0-4) = ? S("evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\\ 7 >= Ar_5 ]", 0-5) = ? S("evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5))", 0-0) = ? S("evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5))", 0-2) = ? S("evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5))", 0-5) = ? orients the transitions evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ] evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ 7 >= Ar_5 ] evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ] evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ] weakly and the transitions evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ] strictly and produces the following problem: 6: T: (Comp: 2*Ar_1 + 60, Cost: 1) evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ 5 >= Ar_5 /\ 7 >= Ar_5 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_5 >= 6 ] (Comp: 2, Cost: 1) evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 2*Ar_1 + 60, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_4 ] (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_5 + 1 ] (Comp: 2, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 30 ] (Comp: Ar_1 + 30, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ 29 >= Ar_0 ] (Comp: 1, Cost: 1) evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(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(evalcomplexstart(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 6 to obtain the following invariants: For symbol evalcomplexbb1in: X_1 - X_2 >= 0 For symbol evalcomplexbb2in: -X_3 + X_6 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_1 + X_5 >= 0 /\ -X_2 + 29 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 + 58 >= 0 /\ -X_1 + 29 >= 0 For symbol evalcomplexbb3in: X_5 - X_6 - 1 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_3 + X_5 - 1 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_1 + X_5 >= 0 /\ -X_2 + 29 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 + 58 >= 0 /\ -X_1 + 29 >= 0 For symbol evalcomplexbb4in: -X_5 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_6 >= 0 /\ -X_1 + X_6 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_1 + X_5 >= 0 /\ -X_2 + 29 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 + 58 >= 0 /\ -X_1 + 29 >= 0 For symbol evalcomplexbb5in: X_1 - X_2 >= 0 /\ X_1 - 30 >= 0 This yielded the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + 30, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ Ar_0 - Ar_1 >= 0 /\ 29 >= Ar_0 ] (Comp: 2, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 30 ] (Comp: ?, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ Ar_4 >= Ar_5 + 1 ] (Comp: 2*Ar_1 + 60, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ Ar_5 >= Ar_4 ] (Comp: 2, Cost: 1) evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 30 >= 0 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_4 - Ar_5 - 1 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_2 + Ar_4 - 1 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ Ar_5 >= 6 ] (Comp: ?, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ Ar_4 - Ar_5 - 1 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_2 + Ar_4 - 1 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ 5 >= Ar_5 /\ 7 >= Ar_5 ] (Comp: 2*Ar_1 + 60, Cost: 1) evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) [ -Ar_4 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_5 >= 0 /\ -Ar_0 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -10*V_2 - 2*V_4 + 348 Pol(evalcomplexstart) = -10*V_2 - 2*V_4 + 348 Pol(evalcomplexbb0in) = -10*V_2 - 2*V_4 + 348 Pol(evalcomplexbb1in) = -10*V_1 - 2*V_3 + 348 Pol(evalcomplexbb2in) = -12*V_1 + 2*V_5 - 2*V_6 + 348 Pol(evalcomplexbb5in) = -10*V_1 - 2*V_3 Pol(evalcomplexbb3in) = -12*V_1 + 2*V_5 - 2*V_6 + 347 Pol(evalcomplexbb4in) = -12*V_1 + 2*V_5 - 2*V_6 + 348 Pol(evalcomplexstop) = -10*V_1 - 2*V_3 orients all transitions weakly and the transitions evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_4 - Ar_5 - 1 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_2 + Ar_4 - 1 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ Ar_5 >= 6 ] evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ Ar_4 - Ar_5 - 1 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_2 + Ar_4 - 1 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ 5 >= Ar_5 /\ 7 >= Ar_5 ] evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ Ar_4 >= Ar_5 + 1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalcomplexstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalcomplexbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + 30, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0, Ar_2)) [ Ar_0 - Ar_1 >= 0 /\ 29 >= Ar_0 ] (Comp: 2, Cost: 1) evalcomplexbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 30 ] (Comp: 10*Ar_1 + 2*Ar_3 + 348, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ Ar_4 >= Ar_5 + 1 ] (Comp: 2*Ar_1 + 60, Cost: 1) evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ Ar_5 >= Ar_4 ] (Comp: 2, Cost: 1) evalcomplexbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 30 >= 0 ] (Comp: 10*Ar_1 + 2*Ar_3 + 348, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 7)) [ Ar_4 - Ar_5 - 1 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_2 + Ar_4 - 1 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ Ar_5 >= 6 ] (Comp: 10*Ar_1 + 2*Ar_3 + 348, Cost: 1) evalcomplexbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 + 2)) [ Ar_4 - Ar_5 - 1 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_2 + Ar_4 - 1 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 /\ 5 >= Ar_5 /\ 7 >= Ar_5 ] (Comp: 2*Ar_1 + 60, Cost: 1) evalcomplexbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalcomplexbb1in(Ar_4 + 2, Ar_1, Ar_5 - 10, Ar_3, Ar_4, Ar_5)) [ -Ar_4 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_5 >= 0 /\ -Ar_0 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_1 + 29 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 + 58 >= 0 /\ -Ar_0 + 29 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 35*Ar_1 + 6*Ar_3 + 1200 Time: 0.350 sec (SMT: 0.269 sec) ---------------------------------------- (2) BOUNDS(1, n^1)