3.12/1.93 WORST_CASE(?, O(n^1)) 3.12/1.94 proof of /export/starexec/sandbox2/output/output_files/bench.koat 3.12/1.94 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.12/1.94 3.12/1.94 3.12/1.94 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 3.12/1.94 3.12/1.94 (0) CpxIntTrs 3.12/1.94 (1) Koat Proof [FINISHED, 578 ms] 3.12/1.94 (2) BOUNDS(1, n^1) 3.12/1.94 3.12/1.94 3.12/1.94 ---------------------------------------- 3.12/1.94 3.12/1.94 (0) 3.12/1.94 Obligation: 3.12/1.94 Complexity Int TRS consisting of the following rules: 3.12/1.94 eval_foo_start(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 eval_foo_bb0_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 eval_foo_bb1_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 > 0 && v_.0 > 0 3.12/1.94 eval_foo_bb1_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb9_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 <= 0 3.12/1.94 eval_foo_bb1_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb9_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.0 <= 0 3.12/1.94 eval_foo_bb2_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.0, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 >= 0 && v_.01 <= 0 3.12/1.94 eval_foo_bb2_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 < 0 3.12/1.94 eval_foo_bb2_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 > 0 3.12/1.94 eval_foo_bb3_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, -(v_.0), v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 < 0 3.12/1.94 eval_foo_bb3_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.0, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 >= 0 3.12/1.94 eval_foo_bb4_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.13, v_.13, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.13 > 0 3.12/1.94 eval_foo_bb4_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb7_in(v_.0, v_.01, v_.13, v_.24, v_.13, v_tmp, v_x, v_xtmp, v_y)) :|: v_.13 <= 0 3.12/1.94 eval_foo_bb5_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb6_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.24 >= v_.01 3.12/1.94 eval_foo_bb5_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.24, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.24 < v_.01 3.12/1.94 eval_foo_bb6_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.13, v_.24 - v_.01, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 eval_foo_bb7_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb8_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.3 < 0 3.12/1.94 eval_foo_bb7_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.3, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.3 >= 0 3.12/1.94 eval_foo_bb8_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb7_in(v_.0, v_.01, v_.13, v_.24, v_.3 - v_.01, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 eval_foo_bb9_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 3.12/1.94 The start-symbols are:[eval_foo_start_9] 3.12/1.94 3.12/1.94 3.12/1.94 ---------------------------------------- 3.12/1.94 3.12/1.94 (1) Koat Proof (FINISHED) 3.12/1.94 YES(?, 16*ar_1 + 48*ar_3 + 8) 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 Initial complexity problem: 3.12/1.94 3.12/1.94 1: T: 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 = 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, -ar_0, ar_5, ar_6)) [ 0 >= ar_2 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_4 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4)) [ 0 >= ar_4 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_5 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_6 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_6, ar_3, ar_4, ar_5, ar_6)) [ ar_6 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - ar_2)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.94 3.12/1.94 start location: koat_start 3.12/1.94 3.12/1.94 leaf cost: 0 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 Testing for reachability in the complexity graph removes the following transitions from problem 1: 3.12/1.94 3.12/1.94 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 = 0 ] 3.12/1.94 3.12/1.94 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 + 1 ] 3.12/1.94 3.12/1.94 evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, -ar_0, ar_5, ar_6)) [ 0 >= ar_2 + 1 ] 3.12/1.94 3.12/1.94 We thus obtain the following problem: 3.12/1.94 3.12/1.94 2: T: 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - ar_2)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_6, ar_3, ar_4, ar_5, ar_6)) [ ar_6 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_6 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_5 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4)) [ 0 >= ar_4 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_4 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.94 3.12/1.94 start location: koat_start 3.12/1.94 3.12/1.94 leaf cost: 0 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 Repeatedly propagating knowledge in problem 2 produces the following problem: 3.12/1.94 3.12/1.94 3: T: 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - ar_2)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_6, ar_3, ar_4, ar_5, ar_6)) [ ar_6 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_6 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_5 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4)) [ 0 >= ar_4 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_4 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.94 3.12/1.94 start location: koat_start 3.12/1.94 3.12/1.94 leaf cost: 0 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 A polynomial rank function with 3.12/1.94 3.12/1.94 Pol(evalfoobb8in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoobb7in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoobb6in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoobb5in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoobb1in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoobb4in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoobb3in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoobb9in) = 1 3.12/1.94 3.12/1.94 Pol(evalfoostop) = 0 3.12/1.94 3.12/1.94 Pol(evalfoobb2in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoobb0in) = 2 3.12/1.94 3.12/1.94 Pol(evalfoostart) = 2 3.12/1.94 3.12/1.94 Pol(koat_start) = 2 3.12/1.94 3.12/1.94 orients all transitions weakly and the transitions 3.12/1.94 3.12/1.94 evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] 3.12/1.94 3.12/1.94 evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 ] 3.12/1.94 3.12/1.94 strictly and produces the following problem: 3.12/1.94 3.12/1.94 4: T: 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - ar_2)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_6, ar_3, ar_4, ar_5, ar_6)) [ ar_6 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_6 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_5 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4)) [ 0 >= ar_4 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_4 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: 2, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 ] 3.12/1.94 3.12/1.94 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.94 3.12/1.94 start location: koat_start 3.12/1.94 3.12/1.94 leaf cost: 0 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 Applied AI with 'oct' on problem 4 to obtain the following invariants: 3.12/1.94 3.12/1.94 For symbol evalfoobb1in: -X_3 + X_4 >= 0 3.12/1.94 3.12/1.94 For symbol evalfoobb2in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 3.12/1.94 3.12/1.94 For symbol evalfoobb3in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 3.12/1.94 3.12/1.94 For symbol evalfoobb4in: X_1 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ -X_1 + X_5 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 3.12/1.94 3.12/1.94 For symbol evalfoobb5in: X_5 - X_6 >= 0 /\ X_1 - X_6 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ -X_1 + X_5 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 3.12/1.94 3.12/1.94 For symbol evalfoobb6in: X_5 - X_6 >= 0 /\ X_1 - X_6 >= 0 /\ X_6 - 1 >= 0 /\ X_5 + X_6 - 2 >= 0 /\ X_4 + X_6 - 2 >= 0 /\ X_3 + X_6 - 2 >= 0 /\ -X_3 + X_6 >= 0 /\ X_1 + X_6 - 2 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ -X_3 + X_5 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ -X_1 + X_5 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 3.12/1.94 3.12/1.94 For symbol evalfoobb7in: -1 >= 0 3.12/1.94 3.12/1.94 For symbol evalfoobb8in: -1 >= 0 3.12/1.94 3.12/1.94 For symbol evalfoobb9in: -X_3 + X_4 >= 0 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 This yielded the following problem: 3.12/1.94 3.12/1.94 5: T: 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_2 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_0 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_4 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_5 >= ar_2 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_5 + 1 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -1 >= 0 /\ 0 >= ar_6 + 1 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_6, ar_3, ar_4, ar_5, ar_6)) [ -1 >= 0 /\ ar_6 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_2 + ar_5 - 2 >= 0 /\ -ar_2 + ar_5 >= 0 /\ ar_0 + ar_5 - 2 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - ar_2)) [ -1 >= 0 ] 3.12/1.95 3.12/1.95 start location: koat_start 3.12/1.95 3.12/1.95 leaf cost: 0 3.12/1.95 3.12/1.95 3.12/1.95 3.12/1.95 Testing for unsatisfiable constraints removes the following transitions from problem 5: 3.12/1.95 3.12/1.95 evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4)) [ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_4 ] 3.12/1.95 3.12/1.95 evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -1 >= 0 /\ 0 >= ar_6 + 1 ] 3.12/1.95 3.12/1.95 evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_6, ar_3, ar_4, ar_5, ar_6)) [ -1 >= 0 /\ ar_6 >= 0 ] 3.12/1.95 3.12/1.95 evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - ar_2)) [ -1 >= 0 ] 3.12/1.95 3.12/1.95 We thus obtain the following problem: 3.12/1.95 3.12/1.95 6: T: 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_2 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_0 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_5 >= ar_2 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_5 + 1 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_2 + ar_5 - 2 >= 0 /\ -ar_2 + ar_5 >= 0 /\ ar_0 + ar_5 - 2 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] 3.12/1.95 3.12/1.95 start location: koat_start 3.12/1.95 3.12/1.95 leaf cost: 0 3.12/1.95 3.12/1.95 3.12/1.95 3.12/1.95 A polynomial rank function with 3.12/1.95 3.12/1.95 Pol(koat_start) = 2*V_2 + 6*V_4 3.12/1.95 3.12/1.95 Pol(evalfoostart) = 2*V_2 + 6*V_4 3.12/1.95 3.12/1.95 Pol(evalfoobb0in) = 2*V_2 + 6*V_4 3.12/1.95 3.12/1.95 Pol(evalfoobb1in) = 2*V_1 + 6*V_3 3.12/1.95 3.12/1.95 Pol(evalfoobb2in) = 2*V_1 + 6*V_3 - 1 3.12/1.95 3.12/1.95 Pol(evalfoobb9in) = 2*V_1 + 6*V_3 3.12/1.95 3.12/1.95 Pol(evalfoobb3in) = 2*V_1 + 6*V_3 - 2 3.12/1.95 3.12/1.95 Pol(evalfoostop) = 2*V_1 + 6*V_3 3.12/1.95 3.12/1.95 Pol(evalfoobb4in) = 6*V_3 + 2*V_5 - 3 3.12/1.95 3.12/1.95 Pol(evalfoobb5in) = 6*V_3 + 2*V_6 - 4 3.12/1.95 3.12/1.95 Pol(evalfoobb6in) = 6*V_3 + 2*V_6 - 5 3.12/1.95 3.12/1.95 orients all transitions weakly and the transitions 3.12/1.95 3.12/1.95 evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_2 + ar_5 - 2 >= 0 /\ -ar_2 + ar_5 >= 0 /\ ar_0 + ar_5 - 2 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] 3.12/1.95 3.12/1.95 evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_5 >= ar_2 ] 3.12/1.95 3.12/1.95 evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= 1 ] 3.12/1.95 3.12/1.95 evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 0 ] 3.12/1.95 3.12/1.95 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] 3.12/1.95 3.12/1.95 evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.95 3.12/1.95 strictly and produces the following problem: 3.12/1.95 3.12/1.95 7: T: 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_2 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_0 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_5 >= ar_2 ] 3.12/1.95 3.12/1.95 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_5 + 1 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_2 + ar_5 - 2 >= 0 /\ -ar_2 + ar_5 >= 0 /\ ar_0 + ar_5 - 2 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] 3.12/1.95 3.12/1.95 start location: koat_start 3.12/1.95 3.12/1.95 leaf cost: 0 3.12/1.95 3.12/1.95 3.12/1.95 3.12/1.95 Repeatedly propagating knowledge in problem 7 produces the following problem: 3.12/1.95 3.12/1.95 8: T: 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.95 3.12/1.95 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_2 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_0 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_2 + ar_3 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 0 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= 1 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_5 >= ar_2 ] 3.12/1.95 3.12/1.95 (Comp: 4*ar_1 + 12*ar_3, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_5 + 1 ] 3.12/1.95 3.12/1.95 (Comp: 2*ar_1 + 6*ar_3, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) [ ar_4 - ar_5 >= 0 /\ ar_0 - ar_5 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_2 + ar_5 - 2 >= 0 /\ -ar_2 + ar_5 >= 0 /\ ar_0 + ar_5 - 2 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ -ar_2 + ar_4 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] 3.12/1.95 3.12/1.95 start location: koat_start 3.12/1.95 3.12/1.95 leaf cost: 0 3.12/1.95 3.12/1.95 3.12/1.95 3.12/1.95 Complexity upper bound 16*ar_1 + 48*ar_3 + 8 3.12/1.95 3.12/1.95 3.12/1.95 3.12/1.95 Time: 0.592 sec (SMT: 0.439 sec) 3.12/1.95 3.12/1.95 3.12/1.95 ---------------------------------------- 3.12/1.95 3.12/1.95 (2) 3.12/1.95 BOUNDS(1, n^1) 3.12/1.96 EOF