4.88/2.24 WORST_CASE(Omega(n^2), O(n^2)) 4.88/2.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.88/2.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.88/2.25 4.88/2.25 4.88/2.25 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 4.88/2.25 4.88/2.25 (0) CpxIntTrs 4.88/2.25 (1) Koat Proof [FINISHED, 112 ms] 4.88/2.25 (2) BOUNDS(1, n^2) 4.88/2.25 (3) Loat Proof [FINISHED, 620 ms] 4.88/2.25 (4) BOUNDS(n^2, INF) 4.88/2.25 4.88/2.25 4.88/2.25 ---------------------------------------- 4.88/2.25 4.88/2.25 (0) 4.88/2.25 Obligation: 4.88/2.25 Complexity Int TRS consisting of the following rules: 4.88/2.25 eval_abc_start(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb0_in(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_bb0_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_0(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_0(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_1(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_1(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_2(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_2(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_3(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_3(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_4(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_4(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb1_in(v_3, 1, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_bb1_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb2_in(v_3, v_i_0, v_i_0, v_n)) :|: v_i_0 <= v_n 4.88/2.25 eval_abc_bb1_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb5_in(v_3, v_i_0, v_j_0, v_n)) :|: v_i_0 > v_n 4.88/2.25 eval_abc_bb2_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb3_in(v_3, v_i_0, v_j_0, v_n)) :|: v_j_0 <= v_n 4.88/2.25 eval_abc_bb2_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb4_in(v_3, v_i_0, v_j_0, v_n)) :|: v_j_0 > v_n 4.88/2.25 eval_abc_bb3_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb2_in(v_3, v_i_0, v_j_0 + 1, v_n)) :|: TRUE 4.88/2.25 eval_abc_bb4_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_8(v_i_0 + 1, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_8(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_9(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_9(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_bb1_in(v_3, v_3, v_j_0, v_n)) :|: TRUE 4.88/2.25 eval_abc_bb5_in(v_3, v_i_0, v_j_0, v_n) -> Com_1(eval_abc_stop(v_3, v_i_0, v_j_0, v_n)) :|: TRUE 4.88/2.25 4.88/2.25 The start-symbols are:[eval_abc_start_4] 4.88/2.25 4.88/2.25 4.88/2.25 ---------------------------------------- 4.88/2.25 4.88/2.25 (1) Koat Proof (FINISHED) 4.88/2.25 YES(?, 155*ar_1 + 10*ar_1^2 + 11) 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Initial complexity problem: 4.88/2.25 4.88/2.25 1: T: 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 4.88/2.25 4.88/2.25 start location: koat_start 4.88/2.25 4.88/2.25 leaf cost: 0 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Repeatedly propagating knowledge in problem 1 produces the following problem: 4.88/2.25 4.88/2.25 2: T: 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 4.88/2.25 4.88/2.25 start location: koat_start 4.88/2.25 4.88/2.25 leaf cost: 0 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 A polynomial rank function with 4.88/2.25 4.88/2.25 Pol(evalabcstart) = 2 4.88/2.25 4.88/2.25 Pol(evalabcbb0in) = 2 4.88/2.25 4.88/2.25 Pol(evalabc0) = 2 4.88/2.25 4.88/2.25 Pol(evalabc1) = 2 4.88/2.25 4.88/2.25 Pol(evalabc2) = 2 4.88/2.25 4.88/2.25 Pol(evalabc3) = 2 4.88/2.25 4.88/2.25 Pol(evalabc4) = 2 4.88/2.25 4.88/2.25 Pol(evalabcbb1in) = 2 4.88/2.25 4.88/2.25 Pol(evalabcbb2in) = 2 4.88/2.25 4.88/2.25 Pol(evalabcbb5in) = 1 4.88/2.25 4.88/2.25 Pol(evalabcbb3in) = 2 4.88/2.25 4.88/2.25 Pol(evalabcbb4in) = 2 4.88/2.25 4.88/2.25 Pol(evalabc8) = 2 4.88/2.25 4.88/2.25 Pol(evalabc9) = 2 4.88/2.25 4.88/2.25 Pol(evalabcstop) = 0 4.88/2.25 4.88/2.25 Pol(koat_start) = 2 4.88/2.25 4.88/2.25 orients all transitions weakly and the transitions 4.88/2.25 4.88/2.25 evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 strictly and produces the following problem: 4.88/2.25 4.88/2.25 3: T: 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 4.88/2.25 4.88/2.25 start location: koat_start 4.88/2.25 4.88/2.25 leaf cost: 0 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 A polynomial rank function with 4.88/2.25 4.88/2.25 Pol(evalabcstart) = V_2 4.88/2.25 4.88/2.25 Pol(evalabcbb0in) = V_2 4.88/2.25 4.88/2.25 Pol(evalabc0) = V_2 4.88/2.25 4.88/2.25 Pol(evalabc1) = V_2 4.88/2.25 4.88/2.25 Pol(evalabc2) = V_2 4.88/2.25 4.88/2.25 Pol(evalabc3) = V_2 4.88/2.25 4.88/2.25 Pol(evalabc4) = V_2 4.88/2.25 4.88/2.25 Pol(evalabcbb1in) = -V_1 + V_2 + 1 4.88/2.25 4.88/2.25 Pol(evalabcbb2in) = -V_1 + V_2 4.88/2.25 4.88/2.25 Pol(evalabcbb5in) = -V_1 + V_2 4.88/2.25 4.88/2.25 Pol(evalabcbb3in) = -V_1 + V_2 4.88/2.25 4.88/2.25 Pol(evalabcbb4in) = -V_1 + V_2 4.88/2.25 4.88/2.25 Pol(evalabc8) = V_2 - V_4 + 1 4.88/2.25 4.88/2.25 Pol(evalabc9) = V_2 - V_4 + 1 4.88/2.25 4.88/2.25 Pol(evalabcstop) = -V_1 + V_2 4.88/2.25 4.88/2.25 Pol(koat_start) = V_2 4.88/2.25 4.88/2.25 orients all transitions weakly and the transition 4.88/2.25 4.88/2.25 evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.88/2.25 4.88/2.25 strictly and produces the following problem: 4.88/2.25 4.88/2.25 4: T: 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ar_1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 4.88/2.25 4.88/2.25 start location: koat_start 4.88/2.25 4.88/2.25 leaf cost: 0 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 A polynomial rank function with 4.88/2.25 4.88/2.25 Pol(evalabcbb4in) = 3 4.88/2.25 4.88/2.25 Pol(evalabc8) = 2 4.88/2.25 4.88/2.25 Pol(evalabcbb3in) = 4 4.88/2.25 4.88/2.25 Pol(evalabcbb2in) = 4 4.88/2.25 4.88/2.25 Pol(evalabc9) = 1 4.88/2.25 4.88/2.25 Pol(evalabcbb1in) = 0 4.88/2.25 4.88/2.25 and size complexities 4.88/2.25 4.88/2.25 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ? 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ? 4.88/2.25 4.88/2.25 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-0) = 1 4.88/2.25 4.88/2.25 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 orients the transitions 4.88/2.25 4.88/2.25 evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 weakly and the transitions 4.88/2.25 4.88/2.25 evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 strictly and produces the following problem: 4.88/2.25 4.88/2.25 5: T: 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ar_1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 4.88/2.25 4.88/2.25 start location: koat_start 4.88/2.25 4.88/2.25 leaf cost: 0 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 A polynomial rank function with 4.88/2.25 4.88/2.25 Pol(evalabcbb3in) = V_2 - V_3 4.88/2.25 4.88/2.25 Pol(evalabcbb2in) = V_2 - V_3 + 1 4.88/2.25 4.88/2.25 and size complexities 4.88/2.25 4.88/2.25 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 4*ar_1 + 272 4.88/2.25 4.88/2.25 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_1 + 4*ar_3 + 1024 4.88/2.25 4.88/2.25 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = 4*ar_1 + 16 4.88/2.25 4.88/2.25 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = 4*ar_1 + 64 4.88/2.25 4.88/2.25 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-0) = 4*ar_1 + 256 4.88/2.25 4.88/2.25 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_1 + 16 4.88/2.25 4.88/2.25 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = 4*ar_1 + 64 4.88/2.25 4.88/2.25 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = 4*ar_1 + 16 4.88/2.25 4.88/2.25 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = 4*ar_1 + 16 4.88/2.25 4.88/2.25 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = 4*ar_1 + 4*ar_3 + 1024 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-0) = 4*ar_1 + 16 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]", 0-3) = 4*ar_1 + 4*ar_3 + 4096 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-0) = 4*ar_1 + 16 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-3) = 4*ar_1 + 4*ar_3 + 1024 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = 4*ar_1 + 68 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ? 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 4*ar_1 + 4*ar_3 + 256 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = 4*ar_1 + 16 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 4*ar_1 + 68 4.88/2.25 4.88/2.25 S("evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = 4*ar_1 + 4*ar_3 + 256 4.88/2.25 4.88/2.25 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-0) = 1 4.88/2.25 4.88/2.25 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 4.88/2.25 4.88/2.25 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.88/2.25 4.88/2.25 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.88/2.25 4.88/2.25 S("evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.88/2.25 4.88/2.25 orients the transitions 4.88/2.25 4.88/2.25 evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 weakly and the transition 4.88/2.25 4.88/2.25 evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 strictly and produces the following problem: 4.88/2.25 4.88/2.25 6: T: 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ar_1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: 5*ar_1^2 + 69*ar_1, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 4.88/2.25 4.88/2.25 start location: koat_start 4.88/2.25 4.88/2.25 leaf cost: 0 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Repeatedly propagating knowledge in problem 6 produces the following problem: 4.88/2.25 4.88/2.25 7: T: 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: ar_1, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: 5*ar_1^2 + 69*ar_1, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ] 4.88/2.25 4.88/2.25 (Comp: 5*ar_1^2 + 69*ar_1, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_0 + 1)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabc9(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 4*ar_1, Cost: 1) evalabc9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcbb1in(ar_3, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 2, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstop(ar_0, ar_1, ar_2, ar_3)) 4.88/2.25 4.88/2.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalabcstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 4.88/2.25 4.88/2.25 start location: koat_start 4.88/2.25 4.88/2.25 leaf cost: 0 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Complexity upper bound 155*ar_1 + 10*ar_1^2 + 11 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Time: 0.173 sec (SMT: 0.132 sec) 4.88/2.25 4.88/2.25 4.88/2.25 ---------------------------------------- 4.88/2.25 4.88/2.25 (2) 4.88/2.25 BOUNDS(1, n^2) 4.88/2.25 4.88/2.25 ---------------------------------------- 4.88/2.25 4.88/2.25 (3) Loat Proof (FINISHED) 4.88/2.25 4.88/2.25 4.88/2.25 ### Pre-processing the ITS problem ### 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Initial linear ITS problem 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 0: evalabcstart -> evalabcbb0in : [], cost: 1 4.88/2.25 4.88/2.25 1: evalabcbb0in -> evalabc0 : [], cost: 1 4.88/2.25 4.88/2.25 2: evalabc0 -> evalabc1 : [], cost: 1 4.88/2.25 4.88/2.25 3: evalabc1 -> evalabc2 : [], cost: 1 4.88/2.25 4.88/2.25 4: evalabc2 -> evalabc3 : [], cost: 1 4.88/2.25 4.88/2.25 5: evalabc3 -> evalabc4 : [], cost: 1 4.88/2.25 4.88/2.25 6: evalabc4 -> evalabcbb1in : A'=1, [], cost: 1 4.88/2.25 4.88/2.25 7: evalabcbb1in -> evalabcbb2in : C'=A, [ B>=A ], cost: 1 4.88/2.25 4.88/2.25 8: evalabcbb1in -> evalabcbb5in : [ A>=1+B ], cost: 1 4.88/2.25 4.88/2.25 9: evalabcbb2in -> evalabcbb3in : [ B>=C ], cost: 1 4.88/2.25 4.88/2.25 10: evalabcbb2in -> evalabcbb4in : [ C>=1+B ], cost: 1 4.88/2.25 4.88/2.25 11: evalabcbb3in -> evalabcbb2in : C'=1+C, [], cost: 1 4.88/2.25 4.88/2.25 12: evalabcbb4in -> evalabc8 : D'=1+A, [], cost: 1 4.88/2.25 4.88/2.25 13: evalabc8 -> evalabc9 : [], cost: 1 4.88/2.25 4.88/2.25 14: evalabc9 -> evalabcbb1in : A'=D, [], cost: 1 4.88/2.25 4.88/2.25 15: evalabcbb5in -> evalabcstop : [], cost: 1 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Removed unreachable and leaf rules: 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 0: evalabcstart -> evalabcbb0in : [], cost: 1 4.88/2.25 4.88/2.25 1: evalabcbb0in -> evalabc0 : [], cost: 1 4.88/2.25 4.88/2.25 2: evalabc0 -> evalabc1 : [], cost: 1 4.88/2.25 4.88/2.25 3: evalabc1 -> evalabc2 : [], cost: 1 4.88/2.25 4.88/2.25 4: evalabc2 -> evalabc3 : [], cost: 1 4.88/2.25 4.88/2.25 5: evalabc3 -> evalabc4 : [], cost: 1 4.88/2.25 4.88/2.25 6: evalabc4 -> evalabcbb1in : A'=1, [], cost: 1 4.88/2.25 4.88/2.25 7: evalabcbb1in -> evalabcbb2in : C'=A, [ B>=A ], cost: 1 4.88/2.25 4.88/2.25 9: evalabcbb2in -> evalabcbb3in : [ B>=C ], cost: 1 4.88/2.25 4.88/2.25 10: evalabcbb2in -> evalabcbb4in : [ C>=1+B ], cost: 1 4.88/2.25 4.88/2.25 11: evalabcbb3in -> evalabcbb2in : C'=1+C, [], cost: 1 4.88/2.25 4.88/2.25 12: evalabcbb4in -> evalabc8 : D'=1+A, [], cost: 1 4.88/2.25 4.88/2.25 13: evalabc8 -> evalabc9 : [], cost: 1 4.88/2.25 4.88/2.25 14: evalabc9 -> evalabcbb1in : A'=D, [], cost: 1 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 ### Simplification by acceleration and chaining ### 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Eliminated locations (on linear paths): 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 4.88/2.25 4.88/2.25 7: evalabcbb1in -> evalabcbb2in : C'=A, [ B>=A ], cost: 1 4.88/2.25 4.88/2.25 22: evalabcbb2in -> evalabcbb2in : C'=1+C, [ B>=C ], cost: 2 4.88/2.25 4.88/2.25 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Accelerating simple loops of location 8. 4.88/2.25 4.88/2.25 Accelerating the following rules: 4.88/2.25 4.88/2.25 22: evalabcbb2in -> evalabcbb2in : C'=1+C, [ B>=C ], cost: 2 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Accelerated rule 22 with metering function 1-C+B, yielding the new rule 26. 4.88/2.25 4.88/2.25 Removing the simple loops: 22. 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Accelerated all simple loops using metering functions (where possible): 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 4.88/2.25 4.88/2.25 7: evalabcbb1in -> evalabcbb2in : C'=A, [ B>=A ], cost: 1 4.88/2.25 4.88/2.25 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 4.88/2.25 4.88/2.25 26: evalabcbb2in -> evalabcbb2in : C'=1+B, [ B>=C ], cost: 2-2*C+2*B 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Chained accelerated rules (with incoming rules): 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 4.88/2.25 4.88/2.25 7: evalabcbb1in -> evalabcbb2in : C'=A, [ B>=A ], cost: 1 4.88/2.25 4.88/2.25 27: evalabcbb1in -> evalabcbb2in : C'=1+B, [ B>=A ], cost: 3-2*A+2*B 4.88/2.25 4.88/2.25 25: evalabcbb2in -> evalabcbb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Eliminated locations (on tree-shaped paths): 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 4.88/2.25 4.88/2.25 28: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1+B, D'=1+A, [ B>=A ], cost: 7-2*A+2*B 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Accelerating simple loops of location 7. 4.88/2.25 4.88/2.25 Accelerating the following rules: 4.88/2.25 4.88/2.25 28: evalabcbb1in -> evalabcbb1in : A'=1+A, C'=1+B, D'=1+A, [ B>=A ], cost: 7-2*A+2*B 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Accelerated rule 28 with metering function 1-A+B, yielding the new rule 29. 4.88/2.25 4.88/2.25 Removing the simple loops: 28. 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Accelerated all simple loops using metering functions (where possible): 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 4.88/2.25 4.88/2.25 29: evalabcbb1in -> evalabcbb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=A ], cost: 8+2*(-1+A-B)*A-8*A-2*(-1+A-B)*B-(-1+A-B)^2+8*B 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Chained accelerated rules (with incoming rules): 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 21: evalabcstart -> evalabcbb1in : A'=1, [], cost: 7 4.88/2.25 4.88/2.25 30: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+B^2+6*B 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Removed unreachable locations (and leaf rules with constant cost): 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 30: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+B^2+6*B 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 ### Computing asymptotic complexity ### 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Fully simplified ITS problem 4.88/2.25 4.88/2.25 Start location: evalabcstart 4.88/2.25 4.88/2.25 30: evalabcstart -> evalabcbb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+B^2+6*B 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Computing asymptotic complexity for rule 30 4.88/2.25 4.88/2.25 Solved the limit problem by the following transformations: 4.88/2.25 4.88/2.25 Created initial limit problem: 4.88/2.25 4.88/2.25 7+B^2+6*B (+), B (+/+!) [not solved] 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 removing all constraints (solved by SMT) 4.88/2.25 4.88/2.25 resulting limit problem: [solved] 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 applying transformation rule (C) using substitution {B==n} 4.88/2.25 4.88/2.25 resulting limit problem: 4.88/2.25 4.88/2.25 [solved] 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Solution: 4.88/2.25 4.88/2.25 B / n 4.88/2.25 4.88/2.25 Resulting cost 7+6*n+n^2 has complexity: Poly(n^2) 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Found new complexity Poly(n^2). 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 Obtained the following overall complexity (w.r.t. the length of the input n): 4.88/2.25 4.88/2.25 Complexity: Poly(n^2) 4.88/2.25 4.88/2.25 Cpx degree: 2 4.88/2.25 4.88/2.25 Solved cost: 7+6*n+n^2 4.88/2.25 4.88/2.25 Rule cost: 7+B^2+6*B 4.88/2.25 4.88/2.25 Rule guard: [ B>=1 ] 4.88/2.25 4.88/2.25 4.88/2.25 4.88/2.25 WORST_CASE(Omega(n^2),?) 4.88/2.25 4.88/2.25 4.88/2.25 ---------------------------------------- 4.88/2.25 4.88/2.25 (4) 4.88/2.25 BOUNDS(n^2, INF) 4.88/2.27 EOF