/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 76 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_.13, v_c, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.13, v_c, v_x, v_y)) :|: TRUE eval_foo_bb1_in(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.02, v_c, v_x, v_y)) :|: v_.01 > 0 eval_foo_bb1_in(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.13, v_c, v_x, v_y)) :|: v_.01 <= 0 eval_foo_bb2_in(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_.13, v_c, v_x, v_y)) :|: v_.13 > 0 eval_foo_bb2_in(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.01, v_.02, v_.13, v_c, v_x, v_y)) :|: v_.13 <= 0 eval_foo_bb3_in(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.13 - 1, v_c, v_x, v_y)) :|: TRUE eval_foo_bb4_in(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 - 1, v_.13, v_.13, v_c, v_x, v_y)) :|: TRUE eval_foo_bb5_in(v_.01, v_.02, v_.13, v_c, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_.02, v_.13, v_c, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 5*Ar_1 + 2*Ar_3 + 11) 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_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_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_4 >= 1 ] (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)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb5in(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 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, 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_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_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_4 >= 1 ] (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)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb5in(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 A polynomial rank function with Pol(evalfoostart) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb2in) = 2 Pol(evalfoobb5in) = 1 Pol(evalfoobb3in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ] strictly and produces the following problem: 3: T: (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_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_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_4 >= 1 ] (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)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfoobb5in(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 A polynomial rank function with Pol(evalfoostart) = V_2 + 1 Pol(evalfoobb0in) = V_2 + 1 Pol(evalfoobb1in) = V_1 + 1 Pol(evalfoobb2in) = V_1 Pol(evalfoobb5in) = V_1 Pol(evalfoobb3in) = V_1 Pol(evalfoobb4in) = V_1 Pol(evalfoostop) = V_1 Pol(koat_start) = V_2 + 1 orients all transitions weakly and the transition evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ] strictly and produces the following problem: 4: T: (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_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: Ar_1 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_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_4 >= 1 ] (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)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfoobb5in(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 A polynomial rank function with Pol(evalfoobb4in) = 1 Pol(evalfoobb1in) = 0 Pol(evalfoobb3in) = 2 Pol(evalfoobb2in) = 2 and size complexities S("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 ]", 0-0) = Ar_0 S("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 ]", 0-1) = Ar_1 S("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 ]", 0-2) = Ar_2 S("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 ]", 0-3) = Ar_3 S("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 ]", 0-4) = Ar_4 S("evalfoobb5in(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) = ? S("evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4))", 0-0) = ? S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4))", 0-2) = ? S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4))", 0-4) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1))", 0-0) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1))", 0-1) = Ar_1 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1))", 0-2) = ? S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1))", 0-3) = Ar_3 S("evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1))", 0-4) = ? S("evalfoobb2in(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_4 ]", 0-0) = ? S("evalfoobb2in(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_4 ]", 0-1) = Ar_1 S("evalfoobb2in(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_4 ]", 0-2) = ? S("evalfoobb2in(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_4 ]", 0-3) = Ar_3 S("evalfoobb2in(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_4 ]", 0-4) = ? S("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_4 >= 1 ]", 0-0) = ? S("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_4 >= 1 ]", 0-1) = Ar_1 S("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_4 >= 1 ]", 0-2) = ? S("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_4 >= 1 ]", 0-3) = Ar_3 S("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_4 >= 1 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]", 0-0) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]", 0-4) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ]", 0-0) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ]", 0-4) = ? S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))", 0-2) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfoostart(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) = Ar_0 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4)) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 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)) [ 0 >= Ar_4 ] 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_4 >= 1 ] weakly and the transitions evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, 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)) [ 0 >= Ar_4 ] strictly and produces the following problem: 5: T: (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_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: Ar_1 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_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_4 >= 1 ] (Comp: 2*Ar_1 + 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)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1)) (Comp: 2*Ar_1 + 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfoobb5in(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 A polynomial rank function with Pol(evalfoostart) = V_4 Pol(evalfoobb0in) = V_4 Pol(evalfoobb1in) = V_3 Pol(evalfoobb2in) = V_5 Pol(evalfoobb5in) = V_3 Pol(evalfoobb3in) = V_5 - 1 Pol(evalfoobb4in) = V_5 Pol(evalfoostop) = V_3 Pol(koat_start) = V_4 orients all transitions weakly and 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_4 >= 1 ] strictly and produces the following problem: 6: T: (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_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: Ar_1 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ] (Comp: Ar_3, 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_4 >= 1 ] (Comp: 2*Ar_1 + 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)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1)) (Comp: 2*Ar_1 + 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfoobb5in(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 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (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_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: Ar_1 + 1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ] (Comp: Ar_3, 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_4 >= 1 ] (Comp: 2*Ar_1 + 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)) [ 0 >= Ar_4 ] (Comp: Ar_3, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1)) (Comp: 2*Ar_1 + 2, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfoobb1in(Ar_0 - 1, Ar_1, Ar_4, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfoobb5in(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 Complexity upper bound 5*Ar_1 + 2*Ar_3 + 11 Time: 0.092 sec (SMT: 0.070 sec) ---------------------------------------- (2) BOUNDS(1, n^1)