/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, EXP). (0) CpxIntTrs (1) Koat Proof [FINISHED, 1781 ms] (2) BOUNDS(1, EXP) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_r >= 0 eval_foo_bb0_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_r < 0 eval_foo_bb1_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(2 * v_r, 2 * v_r, v_4, v_da, v_db, v_r, v_temp)) :|: TRUE eval_foo_bb2_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_.0 >= v_r eval_foo_bb2_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_.0 < v_r eval_foo_bb3_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_3(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: TRUE eval_foo_3(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp), eval_foo_4(v_.0, v_.01, nondef.0, v_da, v_db, v_r, v_temp)) :|: TRUE eval_foo_4(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(v_.0 - 1, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_4 < 0 eval_foo_4(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(v_.0 - 1, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_4 < 0 && v_4 > 0 eval_foo_4(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(v_.0 - 1, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_4 > 0 eval_foo_4(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(v_.01 - 1, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_4 < 0 && v_4 >= 0 && v_4 <= 0 eval_foo_4(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(v_.01 - 1, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: v_4 > 0 && v_4 >= 0 && v_4 <= 0 eval_foo_4(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(v_.0 - 1, v_.01 - 1, v_4, v_da, v_db, v_r, v_temp)) :|: v_4 >= 0 && v_4 <= 0 && v_4 < 0 eval_foo_4(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(v_.0 - 1, v_.01 - 1, v_4, v_da, v_db, v_r, v_temp)) :|: v_4 >= 0 && v_4 <= 0 && v_4 > 0 eval_foo_4(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_bb2_in(v_.01 - 1, v_.01 - 1, v_4, v_da, v_db, v_r, v_temp)) :|: v_4 >= 0 && v_4 <= 0 eval_foo_bb4_in(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp) -> Com_1(eval_foo_stop(v_.0, v_.01, v_4, v_da, v_db, v_r, v_temp)) :|: TRUE The start-symbols are:[eval_foo_start_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2 * pow(2, 2*Ar_0 + 1) * (16*Ar_0 + 4) + pow(2, 2*Ar_0 + 1) * 4 + pow(2, 2*Ar_0 + 1) * (4*Ar_0 + 1) + 36*Ar_0 + 31) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 + 1 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= 1 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= 1 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ 0 >= 1 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ 0 >= 1 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(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(evalfoostart(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: evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 + 1 /\ Ar_3 >= 1 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= 1 /\ Ar_3 = 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= 1 /\ Ar_3 = 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ 0 >= 1 /\ Ar_3 = 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ 0 >= 1 /\ Ar_3 = 0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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(evalfoostart(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) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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(evalfoostart(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(evalfoo4) = 2 Pol(evalfoobb2in) = 2 Pol(evalfoo31) = 2 Pol(evalfoo30) = 0 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoo3) = 2 Pol(evalfoobb3in) = 2 Pol(evalfoobb4in) = 1 Pol(evalfoostop) = 0 Pol(evalfoobb1in) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoostart) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(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) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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(evalfoostart(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 evalfoo3: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoo30: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoo31: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoo4: X_4 - X_5 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoobb1in: X_1 >= 0 For symbol evalfoobb2in: X_1 >= 0 For symbol evalfoobb3in: 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(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] with all transitions in problem 5, the following new transition is obtained: koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] We thus obtain the following problem: 6: T: (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 6: evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) We thus obtain the following problem: 7: T: (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] with all transitions in problem 7, the following new transition is obtained: evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] We thus obtain the following problem: 8: T: (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] with all transitions in problem 8, the following new transition is obtained: evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] We thus obtain the following problem: 9: T: (Comp: ?, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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 transition from problem 9: evalfoo3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] We thus obtain the following problem: 10: T: (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ] with all transitions in problem 10, the following new transition is obtained: evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] We thus obtain the following problem: 11: T: (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 2) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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 transition from problem 11: evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] We thus obtain the following problem: 12: T: (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 ] with all transitions in problem 12, the following new transition is obtained: evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] We thus obtain the following problem: 13: T: (Comp: 1, Cost: 4) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] with all transitions in problem 13, the following new transition is obtained: evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] We thus obtain the following problem: 14: T: (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 4) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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 transition from problem 14: evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) We thus obtain the following problem: 15: T: (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 4) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 ] with all transitions in problem 15, the following new transition is obtained: evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] We thus obtain the following problem: 16: T: (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 4) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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 transition from problem 16: evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] We thus obtain the following problem: 17: T: (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 ] with all transitions in problem 17, the following new transitions are obtained: evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] We thus obtain the following problem: 18: T: (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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(evalfoo4) = 1 Pol(evalfoo30) = 0 Pol(evalfoo31) = 1 Pol(evalfoostop) = 0 Pol(evalfoobb2in) = 1 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoobb0in) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] strictly and produces the following problem: 19: T: (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] with all transitions in problem 19, the following new transitions are obtained: evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] We thus obtain the following problem: 20: T: (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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(evalfoo4) = 1 Pol(evalfoo30) = 0 Pol(evalfoo31) = 1 Pol(evalfoostop) = 0 Pol(evalfoobb2in) = 1 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoobb0in) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] strictly and produces the following problem: 21: T: (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 ] with all transitions in problem 21, the following new transitions are obtained: evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] We thus obtain the following problem: 22: T: (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 3) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 2) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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 22: evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ] We thus obtain the following problem: 23: T: (Comp: ?, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(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(evalfoo4) = 1 Pol(evalfoostop) = 0 Pol(evalfoo30) = 0 Pol(evalfoo31) = 1 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoobb0in) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] strictly and produces the following problem: 24: T: (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] with all transitions in problem 24, the following new transitions are obtained: koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\ 0 >= Ar_0 + 1 ] We thus obtain the following problem: 25: T: (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 3) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 5) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] (Comp: 1, Cost: 2) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 25: evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 + 1 ] We thus obtain the following problem: 26: T: (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 3) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] start location: koat_start leaf cost: 0 A separated polynomial rank function for exponential bounds with Pol(evalfoo4) = 1 Pol(evalfoostop) = 0 Pol(evalfoo30) = 1 Pol(evalfoo31) = 1 Pol(evalVERIFIERnondetintstart) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] strictly and produces the following problem: 27: T: (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 4, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 3) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] start location: koat_start leaf cost: 0 A separated polynomial rank function for exponential bounds with Pol(evalfoo4) = V_3 Pol(evalfoo30) = V_3 Pol(evalfoo31) = V_3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-1) = 2*Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-2) = 2*Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-4) = ? S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-1) = 2*Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-2) = 2*Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-4) = ? S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = ? S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-4) = ? S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = ? S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-3) = 0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-3) = 0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-1) = 2*Ar_0 + 2 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-2) = 2*Ar_0 + 2 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-3) = 0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-4) = 0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-1) = 2*Ar_0 + 2 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-1) = 2*Ar_0 + 2 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-4) = ? orients the transitions evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] weakly and the transition evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] strictly and produces the following problem: 28: T: (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: pow(2, 2*Ar_0 + 1), Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 4, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 3) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoo4) = 2*V_2 Pol(evalfoo30) = 0 Pol(evalfoo31) = 2*V_2 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-1) = 2*Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-2) = 2*Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 0-4) = ? S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-1) = 2*Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-2) = 2*Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\\ Ar_0 >= 0 /\\ 2*Ar_0 >= Ar_0 /\\ 2*Ar_0 >= 0 /\\ 3*Ar_0 >= 0 ]", 1-4) = ? S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\\ 0 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = ? S("evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-4) = ? S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_0 S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-3) = ? S("evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-3) = 0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-3) = 0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_2 - 1 >= Ar_0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 ]", 1-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-1) = 2*Ar_0 + 2 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-2) = 2*Ar_0 + 2 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-3) = 0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 = 0 /\\ Ar_0 >= Ar_2 ]", 0-4) = 0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-1) = 2*Ar_0 + 2 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 0-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-1) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_1 - 1 >= Ar_0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 ]", 1-4) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-0) = Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-1) = 2*Ar_0 + 2 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-2) = 2*Ar_0 S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\\ -Ar_3 + Ar_4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_3 + 1 /\\ Ar_0 >= Ar_1 ]", 0-4) = ? orients the transitions evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] weakly and the transitions evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] strictly and produces the following problem: 29: T: (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_0 >= Ar_1 ] (Comp: pow(2, 2*Ar_0 + 1) * (4*Ar_0 + 1) + 4*Ar_0 + 1, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 + 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 ] (Comp: pow(2, 2*Ar_0 + 1) * (4*Ar_0 + 1) + 4*Ar_0 + 1, Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 /\ Ar_1 - 1 >= Ar_0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] (Comp: 1, Cost: 3) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_0 >= Ar_2 ] (Comp: pow(2, 2*Ar_0 + 1), Cost: 4) evalfoo4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0), evalfoo31(Ar_0, Ar_2 - 1, Ar_2 - 1, Ar_3, Fresh_0)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 = 0 /\ Ar_2 - 1 >= Ar_0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 ] (Comp: pow(2, 2*Ar_0 + 1) * (4*Ar_0 + 1) + 4*Ar_0 + 1, Cost: 1) evalfoo31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoo4(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 4, Cost: 1) evalfoo30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 3) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 6) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalfoo30(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0), evalfoo31(Ar_0, 2*Ar_0, 2*Ar_0, Ar_3, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 0 /\ 2*Ar_0 >= Ar_0 /\ 2*Ar_0 >= 0 /\ 3*Ar_0 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 2 * pow(2, 2*Ar_0 + 1) * (16*Ar_0 + 4) + pow(2, 2*Ar_0 + 1) * 4 + pow(2, 2*Ar_0 + 1) * (4*Ar_0 + 1) + 36*Ar_0 + 31 Time: 1.802 sec (SMT: 1.402 sec) ---------------------------------------- (2) BOUNDS(1, EXP)