/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 82 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: v_x >= 0 && v_y >= 0 eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_x < 0 eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_y < 0 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 - v_.01 > 2 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 - v_.0 > 2 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 - v_.01 <= 2 && v_.01 - v_.0 <= 2 eval_foo_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01, v_x, v_y)) :|: v_.0 < v_.01 eval_foo_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < v_.01 && v_.0 >= v_.01 eval_foo_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01 + 1, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 < v_.01 eval_foo_.critedge_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 + 1, v_x, v_y)) :|: v_.0 >= v_.01 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 8*Ar_0 + 8*Ar_1 + 14) 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, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 /\ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) [ Ar_2 >= Ar_3 /\ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(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 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 1 /\ Ar_2 >= Ar_3 ] evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(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) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (Comp: ?, 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: 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 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (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: 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(evalfoocritedgein) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb2in) = 1 Pol(evalfoostop) = 0 Pol(evalfoobb0in) = 2 Pol(evalfoostart) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb2in(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(evalfoobb2in(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) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\ Ar_2 + 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (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: 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(evalfoobb1in) = -2*V_3 + 2*V_4 + 1 Pol(evalfoocritedgein) = -2*V_3 + 2*V_4 and size complexities 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 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, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-2) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-3) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-3) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 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_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-2) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-3) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-0) = Ar_0 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-2) = Ar_0 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-3) = ? S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-2) = ? S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-3) = Ar_1 orients the transitions evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] weakly and the transitions evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(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) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(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) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (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: 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(evalfoocritedgein) = 2*V_3 - 2*V_4 + 1 Pol(evalfoobb1in) = 2*V_3 - 2*V_4 + 2 and size complexities 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 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, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-2) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-3) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ]", 0-3) = Ar_3 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-2) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ]", 0-3) = ? S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-0) = Ar_0 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-2) = 3*Ar_0 + 3*Ar_1 + 9 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ]", 0-3) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 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_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(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("evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 + 2 >= Ar_2 /\\ Ar_2 + 2 >= Ar_3 ]", 0-3) = ? S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = 3*Ar_0 + 3*Ar_1 + 3*Ar_2 + 81 S("evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-0) = Ar_0 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-1) = Ar_1 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-2) = Ar_0 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]", 0-3) = ? S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-2) = 3*Ar_0 + 3*Ar_1 + 9 S("evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ]", 0-3) = Ar_1 orients the transitions evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] weakly and the transitions evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(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) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= Ar_2 + 1 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(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) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoocritedgein(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 3 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfoobb1in(Ar_0, Ar_1, Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ] (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: 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 Complexity upper bound 8*Ar_0 + 8*Ar_1 + 14 Time: 0.101 sec (SMT: 0.080 sec) ---------------------------------------- (2) BOUNDS(1, n^1)