/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 281 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_bb0_in(v_.01, v_2, v_a, v_max, v_x)) :|: TRUE eval_foo_bb0_in(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_bb1_in(1, v_2, v_a, v_max, v_x)) :|: v_max > 0 eval_foo_bb0_in(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_bb3_in(v_.01, v_2, v_a, v_max, v_x)) :|: v_max <= 0 eval_foo_bb1_in(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_bb2_in(v_.01, v_2, v_a, v_max, v_x)) :|: v_.01 <= v_max eval_foo_bb1_in(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_bb3_in(v_.01, v_2, v_a, v_max, v_x)) :|: v_.01 > v_max eval_foo_bb2_in(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_0(v_.01, v_2, v_a, v_max, v_x)) :|: TRUE eval_foo_0(v_.01, v_2, v_a, v_max, v_x) -> Com_2(eval___VERIFIER_nondet_int_start(v_.01, v_2, v_a, v_max, v_x), eval_foo_1(v_.01, nondef.0, v_a, v_max, v_x)) :|: TRUE eval_foo_1(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_bb1_in(v_.01 + 1, v_2, v_a, v_max, v_x)) :|: v_2 < 0 eval_foo_1(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_bb1_in(v_.01 + 1, v_2, v_a, v_max, v_x)) :|: v_2 > 0 eval_foo_1(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_bb1_in(v_.01 + 1, v_2, v_a, v_max, v_x)) :|: v_2 >= 0 && v_2 <= 0 eval_foo_bb3_in(v_.01, v_2, v_a, v_max, v_x) -> Com_1(eval_foo_stop(v_.01, v_2, v_a, v_max, v_x)) :|: TRUE The start-symbols are:[eval_foo_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 80*Ar_0 + 71) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb3in) = 1 Pol(evalfoobb2in) = 2 Pol(evalfoo0) = 2 Pol(evalfoo00) = 0 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoo01) = 2 Pol(evalfoo1) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfoo0: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo00: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo01: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoo1: X_3 - X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb1in: X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb2in: X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb2in) = 10*V_1 - 6*V_2 + 1 Pol(evalfoo0) = 10*V_1 - 6*V_2 Pol(evalfoobb1in) = 10*V_1 - 6*V_2 + 2 Pol(evalfoo1) = 10*V_1 - 6*V_2 - 3 Pol(evalfoo01) = 10*V_1 - 6*V_2 - 2 Pol(evalfoo00) = 1 Pol(evalVERIFIERnondetintstart) = 0 and size complexities S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-1) = 1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-1) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-1) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = ? S("evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = ? S("evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = ? S("evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = ? S("evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = ? S("evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = ? S("evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = ? S("evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = ? S("evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = ? S("evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = ? S("evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-0) = Ar_0 S("evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-1) = ? S("evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-2) = ? S("evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-3) = ? S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-1) = ? S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-2) = ? S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-3) = ? S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= 1 ]", 0-1) = ? S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= 1 ]", 0-2) = ? S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= 1 ]", 0-3) = ? S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 = 0 ]", 0-0) = Ar_0 S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 = 0 ]", 0-1) = ? S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 = 0 ]", 0-2) = 0 S("evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 = 0 ]", 0-3) = 0 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 ] evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= 1 ] evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_2 + 1 ] evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 = 0 ] evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] weakly and the transitions evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 ] evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= 1 ] evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_2 + 1 ] evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 = 0 ] evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 10*Ar_0 + 8, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 = 0 ] (Comp: 10*Ar_0 + 8, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= 1 ] (Comp: 10*Ar_0 + 8, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_2 + 1 ] (Comp: 10*Ar_0 + 8, Cost: 1) evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_2(evalfoo00(Ar_0, Ar_1, Ar_2, Fresh_0), evalfoo01(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 10*Ar_0 + 8, Cost: 1) evalfoo01(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 10*Ar_0 + 8, Cost: 1) evalfoo00(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 10*Ar_0 + 8, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoo0(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 10*Ar_0 + 8, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 80*Ar_0 + 71 Time: 0.268 sec (SMT: 0.209 sec) ---------------------------------------- (2) BOUNDS(1, n^1)