/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 73 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_wise_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE eval_wise_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_x < 0 eval_wise_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_y < 0 eval_wise_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_x, v_y, v_x, v_y)) :|: v_x >= 0 && v_y >= 0 eval_wise_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 - v_.01 > 2 eval_wise_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 - v_.0 > 2 eval_wise_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 - v_.01 <= 2 && v_.01 - v_.0 <= 2 eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_.0 + 1, v_.01, v_x, v_y)) :|: v_.0 < v_.01 eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < v_.01 && v_.0 >= v_.01 eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_.0 + 1, v_.01 + 1, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 < v_.01 eval_wise_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_.0, v_.01 + 1, v_x, v_y)) :|: v_.0 >= v_.01 eval_wise_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_wise_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE The start-symbols are:[eval_wise_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 8*Ar_0 + 8*Ar_1 + 14) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 /\ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) [ Ar_2 >= Ar_3 /\ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 /\ Ar_2 >= Ar_3 ] evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) [ Ar_2 >= Ar_3 /\ Ar_3 >= Ar_2 + 1 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: ?, Cost: 1) evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: ?, Cost: 1) evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwisecritedgein) = 2 Pol(evalwisebb1in) = 2 Pol(evalwisebb2in) = 1 Pol(evalwisestop) = 0 Pol(evalwisebb0in) = 2 Pol(evalwisestart) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3)) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: 2, Cost: 1) evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwisebb1in) = -2*V_3 + 2*V_4 + 1 Pol(evalwisecritedgein) = -2*V_3 + 2*V_4 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestart(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(evalwisestart(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(evalwisestart(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(evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-3) = Ar_3 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-0) = Ar_0 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-1) = Ar_1 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-2) = Ar_0 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-3) = ? S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-0) = Ar_0 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-1) = Ar_1 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-2) = ? S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-3) = Ar_1 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-0) = Ar_0 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-1) = Ar_1 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-2) = ? S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-3) = ? S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-0) = Ar_0 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-1) = Ar_1 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-2) = Ar_0 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-3) = ? S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-2) = ? S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-3) = Ar_1 orients the transitions evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] weakly and the transitions evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] strictly and produces the following problem: 5: T: (Comp: 2*Ar_0 + 2*Ar_1 + 1, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: 2*Ar_0 + 2*Ar_1 + 1, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: 2, Cost: 1) evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwisecritedgein) = 2*V_3 - 2*V_4 + 1 Pol(evalwisebb1in) = 2*V_3 - 2*V_4 + 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestart(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(evalwisestart(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(evalwisestart(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(evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-3) = Ar_3 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = 3*Ar_0 + 3*Ar_1 + 3*Ar_2 + 81 S("evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-0) = Ar_0 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-1) = Ar_1 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-2) = Ar_0 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-3) = ? S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-0) = Ar_0 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-1) = Ar_1 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-2) = 3*Ar_0 + 3*Ar_1 + 9 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-3) = Ar_1 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-0) = Ar_0 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-1) = Ar_1 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-2) = 3*Ar_0 + 3*Ar_1 + 27 S("evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-3) = ? S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-0) = Ar_0 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-1) = Ar_1 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-2) = Ar_0 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-3) = ? S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-2) = 3*Ar_0 + 3*Ar_1 + 9 S("evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-3) = Ar_1 orients the transitions evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] weakly and the transitions evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] strictly and produces the following problem: 6: T: (Comp: 2*Ar_0 + 2*Ar_1 + 1, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: 2*Ar_0 + 2*Ar_1 + 1, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalwisebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisecritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: 2, Cost: 1) evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwisestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 8*Ar_0 + 8*Ar_1 + 14 Time: 0.101 sec (SMT: 0.079 sec) ---------------------------------------- (2) BOUNDS(1, n^1)