/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 266 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_start_start(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb0_in(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_bb0_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_0(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_0(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_1(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_1(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_2(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_2(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_3(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_3(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_4(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_4(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb1_in(v_m, v_n, v_n, 0)) :|: v_m > 0 eval_start_4(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb5_in(v_m, v_n, v_va_0, v_vb_0)) :|: v_m <= 0 eval_start_bb1_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb2_in(v_m, v_n, v_va_0, v_vb_0)) :|: v_va_0 > 0 eval_start_bb1_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb4_in(v_m, v_n, v_va_0, v_vb_0)) :|: v_va_0 <= 0 eval_start_bb2_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb3_in(v_m, v_n, v_va_0, v_vb_0)) :|: v_vb_0 < v_m eval_start_bb2_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb1_in(v_m, v_n, v_va_0, 0)) :|: v_vb_0 >= v_m eval_start_bb3_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb1_in(v_m, v_n, v_va_0 - 1, v_vb_0 + 1)) :|: TRUE eval_start_bb4_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_stop(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_bb5_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_8(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_8(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_9(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE eval_start_9(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_stop(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE The start-symbols are:[eval_start_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 20*Ar_2 + 19) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstart(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) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalstartstart) = 2 Pol(evalstartbb0in) = 2 Pol(evalstart0) = 2 Pol(evalstart1) = 2 Pol(evalstart2) = 2 Pol(evalstart3) = 2 Pol(evalstart4) = 2 Pol(evalstartbb1in) = 2 Pol(evalstartbb5in) = 0 Pol(evalstartbb2in) = 2 Pol(evalstartbb4in) = 1 Pol(evalstartbb3in) = 2 Pol(evalstartstop) = 0 Pol(evalstart8) = 0 Pol(evalstart9) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) (Comp: 2, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstart(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 evalstart8: -X_1 >= 0 For symbol evalstart9: -X_1 >= 0 For symbol evalstartbb1in: X_4 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb2in: X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb3in: X_1 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb4in: X_4 >= 0 /\ -X_2 + X_4 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_2 + X_3 >= 0 /\ -X_2 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb5in: -X_1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) [ Ar_0 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalstartbb3in) = 5*V_2 + 2*V_4 - 1 Pol(evalstartbb1in) = 5*V_2 + 2*V_4 + 1 Pol(evalstartbb2in) = 5*V_2 + 2*V_4 and size complexities S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ]", 0-0) = Ar_0 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ]", 0-1) = Ar_2 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ]", 0-2) = Ar_2 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ]", 0-3) = 0 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-0) = Ar_0 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-2) = Ar_2 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_2 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= 1 ]", 0-2) = Ar_2 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= 1 ]", 0-3) = Ar_0 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_1 ]", 0-0) = Ar_0 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_1 ]", 0-1) = Ar_2 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_1 ]", 0-2) = Ar_2 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_1 ]", 0-3) = Ar_0 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_3 + 1 ]", 0-1) = Ar_2 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_3 + 1 ]", 0-2) = Ar_2 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_3 + 1 ]", 0-3) = Ar_0 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_0 ]", 0-0) = Ar_0 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_0 ]", 0-1) = Ar_2 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_0 ]", 0-2) = Ar_2 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_0 ]", 0-3) = 0 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) [ Ar_0 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) [ Ar_0 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_2 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) [ Ar_0 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_2 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) [ Ar_0 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = Ar_0 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ -Ar_1 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ -Ar_1 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_2 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ -Ar_1 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_2 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ -Ar_1 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = Ar_0 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-2) = Ar_2 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-3) = Ar_3 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-2) = Ar_2 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-3) = Ar_3 S("evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-2) = Ar_2 S("evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstart(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(evalstartstart(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(evalstartstart(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(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) [ Ar_0 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_0 ] evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] weakly and the transitions evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) [ Ar_0 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_0 ] evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalstart9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart9(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 5*Ar_2 + 1, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1 - 1, Ar_2, Ar_3 + 1)) [ Ar_0 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 5*Ar_2 + 1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_0 ] (Comp: 5*Ar_2 + 1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ] (Comp: 5*Ar_2 + 1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb1in(Ar_0, Ar_2, Ar_2, 0)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 20*Ar_2 + 19 Time: 0.331 sec (SMT: 0.259 sec) ---------------------------------------- (2) BOUNDS(1, n^1)