24.92/17.60	WORST_CASE(?, O(n^2))
24.92/17.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
24.92/17.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
24.92/17.62	
24.92/17.62	
24.92/17.62	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
24.92/17.62	
24.92/17.62	(0) CpxIntTrs
24.92/17.62	(1) Koat Proof [FINISHED, 454 ms]
24.92/17.62	(2) BOUNDS(1, n^2)
24.92/17.62	
24.92/17.62	
24.92/17.62	----------------------------------------
24.92/17.62	
24.92/17.62	(0)
24.92/17.62	Obligation:
24.92/17.62	Complexity Int TRS consisting of the following rules:
24.92/17.62	eval_realheapsort_step1_start(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb0_in(v_33, v_N, v_j_0, v_k_0)) :|: TRUE
24.92/17.62	eval_realheapsort_step1_bb0_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_0(v_33, v_N, v_j_0, v_k_0)) :|: TRUE
24.92/17.62	eval_realheapsort_step1_0(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_1(v_33, v_N, v_j_0, v_k_0)) :|: TRUE
24.92/17.62	eval_realheapsort_step1_1(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0)) :|: TRUE
24.92/17.62	eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, 1)) :|: v_N > 2
24.92/17.62	eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0)) :|: v_N <= 2
24.92/17.62	eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, v_k_0, v_k_0)) :|: v_k_0 <= v_N - 1
24.92/17.62	eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0)) :|: v_k_0 > v_N - 1
24.92/17.62	eval_realheapsort_step1_bb2_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 > 0
24.92/17.62	eval_realheapsort_step1_bb2_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 <= 0
24.92/17.62	eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_0 >= 0 && nondef_0 <= 0
24.92/17.62	eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_0 >= 0 && v_j_0 - 2 * nondef_0 + 1 >= 0 && v_j_0 - 2 * nondef_0 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_0 <= 0 && -(v_j_0) + 2 * nondef_0 - 1 >= 0 && -(v_j_0) + 2 * nondef_0 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_0 >= 0 && nondef_0 <= 0
24.92/17.62	eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_0 >= 0 && v_j_0 - 2 * nondef_0 + 1 >= 0 && v_j_0 - 2 * nondef_0 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_0 <= 0 && -(v_j_0) + 2 * nondef_0 - 1 >= 0 && -(v_j_0) + 2 * nondef_0 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2
24.92/17.62	eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2
24.92/17.62	eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_28(v_k_0 + 1, v_N, v_j_0, v_k_0)) :|: TRUE
24.92/17.62	eval_realheapsort_step1_28(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_29(v_33, v_N, v_j_0, v_k_0)) :|: TRUE
24.92/17.62	eval_realheapsort_step1_29(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_33)) :|: TRUE
24.92/17.62	eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_stop(v_33, v_N, v_j_0, v_k_0)) :|: TRUE
24.92/17.62	
24.92/17.62	The start-symbols are:[eval_realheapsort_step1_start_4]
24.92/17.62	
24.92/17.62	
24.92/17.62	----------------------------------------
24.92/17.62	
24.92/17.62	(1) Koat Proof (FINISHED)
24.92/17.62	YES(?, 5931*ar_0 + 72*ar_0^2 + 5869)
24.92/17.62	
24.92/17.62	
24.92/17.62	
24.92/17.62	Initial complexity problem:
24.92/17.62	
24.92/17.62	1:	T:
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ 0 >= f /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= g /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= g /\ 0 >= e /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ ar_2 >= 0 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ ar_2 >= 0 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ 0 >= e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ 0 >= f /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ 0 >= g /\ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ 0 >= g /\ 0 >= e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
24.92/17.62	
24.92/17.62		start location:	koat_start
24.92/17.62	
24.92/17.62		leaf cost:	0
24.92/17.62	
24.92/17.62	
24.92/17.62	
24.92/17.62	Testing for reachability in the complexity graph removes the following transitions from problem 1:
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ ar_2 + 1 = 0 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ 0 >= f /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= g /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= g /\ 0 >= e /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ ar_2 >= 0 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ ar_2 >= 0 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ 0 >= e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ 0 >= f /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ 0 >= g /\ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ 0 >= g /\ 0 >= e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ]
24.92/17.62	
24.92/17.62	We thus obtain the following problem:
24.92/17.62	
24.92/17.62	2:	T:
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
24.92/17.62	
24.92/17.62		start location:	koat_start
24.92/17.62	
24.92/17.62		leaf cost:	0
24.92/17.62	
24.92/17.62	
24.92/17.62	
24.92/17.62	Repeatedly propagating knowledge in problem 2 produces the following problem:
24.92/17.62	
24.92/17.62	3:	T:
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
24.92/17.62	
24.92/17.62		start location:	koat_start
24.92/17.62	
24.92/17.62		leaf cost:	0
24.92/17.62	
24.92/17.62	
24.92/17.62	
24.92/17.62	A polynomial rank function with
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb1in) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb5in) = 1
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep129) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep128) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb4in) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb2in) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1critedgein) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb3in) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1stop) = 0
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep12) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep11) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep10) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb0in) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1start) = 2
24.92/17.62	
24.92/17.62		Pol(koat_start) = 2
24.92/17.62	
24.92/17.62	orients all transitions weakly and the transitions
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
24.92/17.62	
24.92/17.62	strictly and produces the following problem:
24.92/17.62	
24.92/17.62	4:	T:
24.92/17.62	
24.92/17.62			(Comp: 2, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.62	
24.92/17.62			(Comp: 2, Cost: 1)    evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)    evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
24.92/17.62	
24.92/17.62		start location:	koat_start
24.92/17.62	
24.92/17.62		leaf cost:	0
24.92/17.62	
24.92/17.62	
24.92/17.62	
24.92/17.62	A polynomial rank function with
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1critedgein) = V_1 - V_2 - 1
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep128) = V_1 - V_4
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb4in) = V_1 - V_2 - 1
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb2in) = V_1 - V_2 - 1
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb3in) = V_1 - V_2 - 1
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb1in) = V_1 - V_2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep129) = V_1 - V_4
24.92/17.62	
24.92/17.62	and size complexities
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-1) = 1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ?
24.92/17.62	
24.92/17.62	orients the transitions
24.92/17.62	
24.92/17.62		evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62		evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62	weakly and the transition
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.62	
24.92/17.62	strictly and produces the following problem:
24.92/17.62	
24.92/17.62	5:	T:
24.92/17.62	
24.92/17.62			(Comp: 2, Cost: 1)           evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)           evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)           evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)           evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)           evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)           evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)           evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)           evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)           evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.62	
24.92/17.62			(Comp: 2, Cost: 1)           evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ar_0 + 1, Cost: 1)    evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)           evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)           evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)           evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)           evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)           evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)           evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
24.92/17.62	
24.92/17.62		start location:	koat_start
24.92/17.62	
24.92/17.62		leaf cost:	0
24.92/17.62	
24.92/17.62	
24.92/17.62	
24.92/17.62	A polynomial rank function with
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1critedgein) = 3
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep128) = 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb4in) = 4
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb2in) = 4
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb3in) = 4
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep129) = 1
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb1in) = 0
24.92/17.62	
24.92/17.62	and size complexities
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-1) = 1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-3) = ar_3
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-3) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = ?
24.92/17.62	
24.92/17.62		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ?
24.92/17.62	
24.92/17.62	orients the transitions
24.92/17.62	
24.92/17.62		evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62		evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62	weakly and the transitions
24.92/17.62	
24.92/17.62		evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62		evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62		evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62	strictly and produces the following problem:
24.92/17.62	
24.92/17.62	6:	T:
24.92/17.62	
24.92/17.62			(Comp: 2, Cost: 1)             evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: 4*ar_0 + 4, Cost: 1)    evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 4*ar_0 + 4, Cost: 1)    evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)             evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: 4*ar_0 + 4, Cost: 1)    evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.62	
24.92/17.62			(Comp: 4*ar_0 + 4, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)             evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: 4*ar_0 + 4, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.62	
24.92/17.62			(Comp: ?, Cost: 1)             evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.62	
24.92/17.62			(Comp: 2, Cost: 1)             evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: ar_0 + 1, Cost: 1)      evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)             evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)             evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)             evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)             evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)             evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 1)             evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))
24.92/17.62	
24.92/17.62			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
24.92/17.62	
24.92/17.62		start location:	koat_start
24.92/17.62	
24.92/17.62		leaf cost:	0
24.92/17.62	
24.92/17.62	
24.92/17.62	
24.92/17.62	A polynomial rank function with
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb4in) = 3*V_3 + 1
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb2in) = 6*V_3 + 2
24.92/17.62	
24.92/17.62		Pol(evalrealheapsortstep1bb3in) = 3*V_3 + 3
24.92/17.62	
24.92/17.62	and size complexities
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
24.92/17.62	
24.92/17.62		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-1) = 1
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-2) = ar_2
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-3) = ar_3
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-1) = ar_1
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-2) = ar_2
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-3) = ar_3
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 4*ar_0 + 324
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 1280
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = 4*ar_0 + 4*ar_1 + 1280
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = 4*ar_0 + 4*ar_2 + 5373952
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_0 + 4*ar_3 + 5120
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = 4*ar_0 + 1312
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 5120
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-1) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-2) = 4*ar_0 + 5248
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-3) = 4*ar_0 + 4*ar_3 + 20480
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = 4*ar_0 + 1312
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = 4*ar_0 + 4*ar_3 + 5120
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = 4*ar_0 + 5248
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = 4*ar_0 + 4*ar_3 + 20480
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-1) = 4*ar_0 + 320
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-2) = 4*ar_0 + 20992
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-3) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = 4*ar_0 + 1312
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = 4*ar_0 + 4*ar_3 + 5120
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-1) = 4*ar_0 + 1280
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-2) = 4*ar_0 + 83968
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-1) = 4*ar_0 + 80
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-2) = 4*ar_0 + 335872
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-3) = 4*ar_0 + 320
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ar_0
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = 4*ar_0 + 320
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 4*ar_0 + 1343488
24.92/17.63	
24.92/17.63		S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = 4*ar_0 + 1280
24.92/17.63	
24.92/17.63	orients the transitions
24.92/17.63	
24.92/17.63		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.63	
24.92/17.63		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.63	
24.92/17.63		evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.63	
24.92/17.63	weakly and the transitions
24.92/17.63	
24.92/17.63		evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.63	
24.92/17.63		evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.63	
24.92/17.63		evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.63	
24.92/17.63	strictly and produces the following problem:
24.92/17.63	
24.92/17.63	7:	T:
24.92/17.63	
24.92/17.63			(Comp: 2, Cost: 1)                               evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
24.92/17.63	
24.92/17.63			(Comp: 4*ar_0 + 4, Cost: 1)                      evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))
24.92/17.63	
24.92/17.63			(Comp: 4*ar_0 + 4, Cost: 1)                      evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))
24.92/17.63	
24.92/17.63			(Comp: 24*ar_0^2 + 1970*ar_0 + 1946, Cost: 1)    evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.63	
24.92/17.63			(Comp: 4*ar_0 + 4, Cost: 1)                      evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))
24.92/17.63	
24.92/17.63			(Comp: 4*ar_0 + 4, Cost: 1)                      evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.63	
24.92/17.63			(Comp: 24*ar_0^2 + 1970*ar_0 + 1946, Cost: 1)    evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ]
24.92/17.63	
24.92/17.63			(Comp: 4*ar_0 + 4, Cost: 1)                      evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
24.92/17.63	
24.92/17.63			(Comp: 24*ar_0^2 + 1970*ar_0 + 1946, Cost: 1)    evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
24.92/17.63	
24.92/17.63			(Comp: 2, Cost: 1)                               evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))
24.92/17.63	
24.92/17.63			(Comp: ar_0 + 1, Cost: 1)                        evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]
24.92/17.63	
24.92/17.63			(Comp: 1, Cost: 1)                               evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]
24.92/17.63	
24.92/17.63			(Comp: 1, Cost: 1)                               evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]
24.92/17.63	
24.92/17.63			(Comp: 1, Cost: 1)                               evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))
24.92/17.63	
24.92/17.63			(Comp: 1, Cost: 1)                               evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))
24.92/17.63	
24.92/17.63			(Comp: 1, Cost: 1)                               evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))
24.92/17.63	
24.92/17.63			(Comp: 1, Cost: 1)                               evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))
24.92/17.63	
24.92/17.63			(Comp: 1, Cost: 0)                               koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
24.92/17.63	
24.92/17.63		start location:	koat_start
24.92/17.63	
24.92/17.63		leaf cost:	0
24.92/17.63	
24.92/17.63	
24.92/17.63	
24.92/17.63	Complexity upper bound 5931*ar_0 + 72*ar_0^2 + 5869
24.92/17.63	
24.92/17.63	
24.92/17.63	
24.92/17.63	Time: 0.399 sec (SMT: 0.294 sec)
24.92/17.63	
24.92/17.63	
24.92/17.63	----------------------------------------
24.92/17.63	
24.92/17.63	(2)
24.92/17.63	BOUNDS(1, n^2)
24.92/17.65	EOF