/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^2)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 76 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speedNestedMultipleDep_start(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb0_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: TRUE eval_speedNestedMultipleDep_bb0_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, 0, v_y.0)) :|: TRUE eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb2_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 < v_n eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb5_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 >= v_n eval_speedNestedMultipleDep_bb2_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb3_in(v_x.0 + 1, v_m, v_n, v_x.0, 0)) :|: TRUE eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb4_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_y.0 < v_m eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_1, v_y.0)) :|: v_y.0 >= v_m eval_speedNestedMultipleDep_bb4_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0 + 1)) :|: TRUE eval_speedNestedMultipleDep_bb5_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_stop(v_1, v_m, v_n, v_x.0, v_y.0)) :|: TRUE The start-symbols are:[eval_speedNestedMultipleDep_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 3*Ar_1 + 2*Ar_1*Ar_4 + 6) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart) = 2 Pol(evalspeedNestedMultipleDepbb0in) = 2 Pol(evalspeedNestedMultipleDepbb1in) = 2 Pol(evalspeedNestedMultipleDepbb2in) = 2 Pol(evalspeedNestedMultipleDepbb5in) = 1 Pol(evalspeedNestedMultipleDepbb3in) = 2 Pol(evalspeedNestedMultipleDepbb4in) = 2 Pol(evalspeedNestedMultipleDepstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart) = V_2 Pol(evalspeedNestedMultipleDepbb0in) = V_2 Pol(evalspeedNestedMultipleDepbb1in) = -V_1 + V_2 Pol(evalspeedNestedMultipleDepbb2in) = -V_1 + V_2 - 1 Pol(evalspeedNestedMultipleDepbb5in) = -V_1 + V_2 Pol(evalspeedNestedMultipleDepbb3in) = V_2 - V_3 Pol(evalspeedNestedMultipleDepbb4in) = V_2 - V_3 Pol(evalspeedNestedMultipleDepstop) = -V_1 + V_2 Pol(koat_start) = V_2 orients all transitions weakly and the transition evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepbb4in) = 1 Pol(evalspeedNestedMultipleDepbb3in) = 1 Pol(evalspeedNestedMultipleDepbb1in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-3) = 0 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 0 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] weakly and the transition evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepbb4in) = -V_4 + V_5 - 1 Pol(evalspeedNestedMultipleDepbb3in) = -V_4 + V_5 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-3) = 0 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 0 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] weakly and the transition evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: Ar_1*Ar_4, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: Ar_1*Ar_4, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: Ar_1*Ar_4, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 3*Ar_1 + 2*Ar_1*Ar_4 + 6 Time: 0.095 sec (SMT: 0.071 sec) ---------------------------------------- (2) BOUNDS(1, n^2)