/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 383 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_rsd_start(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb0_in(v_4, v_da.0, v_db.0, v_r)) :|: TRUE eval_rsd_bb0_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb1_in(v_4, v_da.0, v_db.0, v_r)) :|: v_r >= 0 eval_rsd_bb0_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb4_in(v_4, v_da.0, v_db.0, v_r)) :|: v_r < 0 eval_rsd_bb1_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, 2 * v_r, 2 * v_r, v_r)) :|: TRUE eval_rsd_bb2_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb3_in(v_4, v_da.0, v_db.0, v_r)) :|: v_da.0 >= v_r eval_rsd_bb2_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb4_in(v_4, v_da.0, v_db.0, v_r)) :|: v_da.0 < v_r eval_rsd_bb3_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_3(v_4, v_da.0, v_db.0, v_r)) :|: TRUE eval_rsd_3(v_4, v_da.0, v_db.0, v_r) -> Com_2(eval_nondet_start(v_4, v_da.0, v_db.0, v_r), eval_rsd_4(nondef.0, v_da.0, v_db.0, v_r)) :|: TRUE eval_rsd_4(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, v_da.0 - 1, v_db.0, v_r)) :|: v_4 > 0 eval_rsd_4(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, v_db.0 - 1, v_db.0, v_r)) :|: v_4 > 0 && v_4 <= 0 eval_rsd_4(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, v_da.0 - 1, v_da.0, v_r)) :|: v_4 <= 0 && v_4 > 0 eval_rsd_4(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, v_db.0 - 1, v_da.0, v_r)) :|: v_4 <= 0 eval_rsd_bb4_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_stop(v_4, v_da.0, v_db.0, v_r)) :|: TRUE The start-symbols are:[eval_rsd_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 168*Ar_0 + 50) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 /\ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_1, Ar_3, Ar_4)) [ 0 >= Ar_3 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 /\ 0 >= Ar_3 ] evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_1, Ar_3, Ar_4)) [ 0 >= Ar_3 /\ Ar_3 >= 1 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrsd4) = 2 Pol(evalrsdbb2in) = 2 Pol(evalrsd31) = 2 Pol(evalrsd30) = 0 Pol(evalnondetstart) = 0 Pol(evalrsd3) = 2 Pol(evalrsdbb3in) = 2 Pol(evalrsdbb4in) = 1 Pol(evalrsdstop) = 0 Pol(evalrsdbb1in) = 2 Pol(evalrsdbb0in) = 2 Pol(evalrsdstart) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol evalrsd3: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalrsd30: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalrsd31: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalrsd4: X_4 - X_5 >= 0 /\ -X_4 + X_5 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalrsdbb1in: X_1 >= 0 For symbol evalrsdbb2in: X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0 For symbol evalrsdbb3in: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 This yielded the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrsdbb3in) = 6*V_2 + 6*V_3 + 5 Pol(evalrsd3) = 6*V_2 + 6*V_3 + 4 Pol(evalrsdbb2in) = 6*V_2 + 6*V_3 + 6 Pol(evalrsd4) = 6*V_2 + 6*V_3 + 1 Pol(evalrsd31) = 6*V_2 + 6*V_3 + 2 Pol(evalrsd30) = 1 Pol(evalnondetstart) = 0 and size complexities S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 ]", 0-0) = Ar_0 S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 ]", 0-1) = 2*Ar_0 + 8 S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 ]", 0-2) = 2*Ar_0 + 8 S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 ]", 0-3) = ? S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 ]", 0-4) = ? S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 ]", 0-1) = 2*Ar_0 + 8 S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 ]", 0-2) = 2*Ar_0 + 8 S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 ]", 0-3) = ? S("evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 ]", 0-4) = ? S("evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 + 8 S("evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = ? S("evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-4) = ? S("evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 + 16 S("evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 + 16 S("evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = ? S("evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-4) = ? S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 + 8 S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = ? S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-4) = ? S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 1-0) = Ar_0 S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 1-1) = 2*Ar_0 + 8 S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 1-2) = 2*Ar_0 + 8 S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 1-3) = ? S("evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 1-4) = ? S("evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 + 8 S("evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = ? S("evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-4) = ? S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-1) = 2*Ar_0 + 16 S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-2) = 2*Ar_0 + 16 S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-0) = Ar_0 S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-1) = 2*Ar_0 + 8 S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-2) = 2*Ar_0 + 8 S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = 2*Ar_0 + 2*Ar_1 + 32 S("evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = 2*Ar_0 + 2*Ar_2 + 32 S("evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 S("evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 S("evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-3) = Ar_3 S("evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-4) = Ar_4 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-2) = Ar_2 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-3) = Ar_3 S("evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ]", 0-4) = Ar_4 S("evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 orients the transitions evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] weakly and the transitions evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalrsdstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalrsdbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalrsdbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 24*Ar_0 + 6, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalrsdbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: 24*Ar_0 + 6, Cost: 1) evalrsdbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 24*Ar_0 + 6, Cost: 1) evalrsd3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 24*Ar_0 + 6, Cost: 1) evalrsd30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 24*Ar_0 + 6, Cost: 1) evalrsd31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsd4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 24*Ar_0 + 6, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: 24*Ar_0 + 6, Cost: 1) evalrsd4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrsdbb2in(Ar_0, Ar_2 - 1, Ar_1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] start location: koat_start leaf cost: 0 Complexity upper bound 168*Ar_0 + 50 Time: 0.361 sec (SMT: 0.285 sec) ---------------------------------------- (2) BOUNDS(1, n^1)