10.62/4.72	WORST_CASE(Omega(n^1), O(n^1))
10.68/4.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
10.68/4.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.68/4.73	
10.68/4.73	
10.68/4.73	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
10.68/4.73	
10.68/4.73	(0) CpxIntTrs
10.68/4.73	(1) Koat Proof [FINISHED, 524 ms]
10.68/4.73	(2) BOUNDS(1, n^1)
10.68/4.73	(3) Loat Proof [FINISHED, 3041 ms]
10.68/4.73	(4) BOUNDS(n^1, INF)
10.68/4.73	
10.68/4.73	
10.68/4.73	----------------------------------------
10.68/4.73	
10.68/4.73	(0)
10.68/4.73	Obligation:
10.68/4.73	Complexity Int TRS consisting of the following rules:
10.68/4.73	eval_random2d_start(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb0_in(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_bb0_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_0(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_0(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_1(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_1(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_2(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_2(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_3(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_3(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_4(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_4(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_5(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_5(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_6(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_6(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_7(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_7(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_8(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_8(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_9(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_9(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_10(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_10(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, 0)) :|: TRUE
10.68/4.73	eval_random2d_bb1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb2_in(v_1, v_2, v_N, v_i_0)) :|: v_i_0 < v_N
10.68/4.73	eval_random2d_bb1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb8_in(v_1, v_2, v_N, v_i_0)) :|: v_i_0 >= v_N
10.68/4.73	eval_random2d_bb2_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_12(v_i_0 + 1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_12(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_13(v_1, nondef_0, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_13(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb3_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 0 && v_2 <= 3
10.68/4.73	eval_random2d_13(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: v_2 < 0
10.68/4.73	eval_random2d_13(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: v_2 > 3
10.68/4.73	eval_random2d_bb3_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NodeBlock9_in(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	eval_random2d_NodeBlock9_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NodeBlock_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 2
10.68/4.73	eval_random2d_NodeBlock9_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NodeBlock7_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 2
10.68/4.73	eval_random2d_NodeBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_LeafBlock_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 1
10.68/4.73	eval_random2d_NodeBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_LeafBlock1_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 1
10.68/4.73	eval_random2d_LeafBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb4_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 0 && v_2 <= 0
10.68/4.73	eval_random2d_LeafBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 0
10.68/4.73	eval_random2d_LeafBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 > 0
10.68/4.73	eval_random2d_bb4_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE
10.68/4.73	eval_random2d_LeafBlock1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb5_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 1 && v_2 <= 1
10.68/4.73	eval_random2d_LeafBlock1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 1
10.68/4.73	eval_random2d_LeafBlock1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 > 1
10.68/4.73	eval_random2d_bb5_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE
10.68/4.73	eval_random2d_NodeBlock7_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_LeafBlock3_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 3
10.68/4.73	eval_random2d_NodeBlock7_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_LeafBlock5_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 3
10.68/4.73	eval_random2d_LeafBlock3_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb6_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 2 && v_2 <= 2
10.68/4.73	eval_random2d_LeafBlock3_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 2
10.68/4.73	eval_random2d_LeafBlock3_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 > 2
10.68/4.73	eval_random2d_bb6_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE
10.68/4.73	eval_random2d_LeafBlock5_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb7_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 3 && v_2 <= 3
10.68/4.73	eval_random2d_LeafBlock5_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 3
10.68/4.73	eval_random2d_LeafBlock5_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 > 3
10.68/4.73	eval_random2d_bb7_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE
10.68/4.73	eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE
10.68/4.73	eval_random2d_bb8_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_stop(v_1, v_2, v_N, v_i_0)) :|: TRUE
10.68/4.73	
10.68/4.73	The start-symbols are:[eval_random2d_start_4]
10.68/4.73	
10.68/4.73	
10.68/4.73	----------------------------------------
10.68/4.73	
10.68/4.73	(1) Koat Proof (FINISHED)
10.68/4.73	YES(?, 29*ar_1 + 17)
10.68/4.73	
10.68/4.73	
10.68/4.73	
10.68/4.73	Initial complexity problem:
10.68/4.73	
10.68/4.73	1:	T:
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d0(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d1(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d2(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d3(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d4(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d5(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d6(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d7(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d8(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d9(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d10(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d12(ar_0, ar_1, ar_0 + 1, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d13(ar_0, ar_1, ar_2, e))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ 3 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
10.68/4.73	
10.68/4.73		start location:	koat_start
10.68/4.73	
10.68/4.73		leaf cost:	0
10.68/4.73	
10.68/4.73	
10.68/4.73	
10.68/4.73	Testing for reachability in the complexity graph removes the following transitions from problem 1:
10.68/4.73	
10.68/4.73		evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
10.68/4.73	
10.68/4.73		evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
10.68/4.73	
10.68/4.73		evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
10.68/4.73	
10.68/4.73		evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
10.68/4.73	
10.68/4.73	We thus obtain the following problem:
10.68/4.73	
10.68/4.73	2:	T:
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ 3 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d13(ar_0, ar_1, ar_2, e))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d12(ar_0, ar_1, ar_0 + 1, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d10(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d9(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d8(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d7(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d6(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d5(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d4(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d3(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d2(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d1(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d0(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
10.68/4.73	
10.68/4.73		start location:	koat_start
10.68/4.73	
10.68/4.73		leaf cost:	0
10.68/4.73	
10.68/4.73	
10.68/4.73	
10.68/4.73	Repeatedly propagating knowledge in problem 2 produces the following problem:
10.68/4.73	
10.68/4.73	3:	T:
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ 3 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d13(ar_0, ar_1, ar_2, e))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d12(ar_0, ar_1, ar_0 + 1, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d10(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d9(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d8(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d7(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d6(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d5(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d4(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d3(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d2(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d1(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d0(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
10.68/4.73	
10.68/4.73		start location:	koat_start
10.68/4.73	
10.68/4.73		leaf cost:	0
10.68/4.73	
10.68/4.73	
10.68/4.73	
10.68/4.73	A polynomial rank function with
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb7in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb1in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb6in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb5in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dNewDefaultin) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb4in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dLeafBlock5in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dLeafBlock3in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dLeafBlock1in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dLeafBlockin) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dNodeBlock7in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dNodeBlockin) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dNodeBlock9in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb3in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d13) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d12) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb8in) = 1
10.68/4.73	
10.68/4.73		Pol(evalrandom2dstop) = 0
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb2in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d10) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d9) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d8) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d7) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d6) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d5) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d4) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d3) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d2) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d1) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2d0) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dbb0in) = 2
10.68/4.73	
10.68/4.73		Pol(evalrandom2dstart) = 2
10.68/4.73	
10.68/4.73		Pol(koat_start) = 2
10.68/4.73	
10.68/4.73	orients all transitions weakly and the transitions
10.68/4.73	
10.68/4.73		evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73		evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
10.68/4.73	
10.68/4.73	strictly and produces the following problem:
10.68/4.73	
10.68/4.73	4:	T:
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ 3 >= ar_3 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2d12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d13(ar_0, ar_1, ar_2, e))
10.68/4.73	
10.68/4.73			(Comp: 2, Cost: 1)    evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d12(ar_0, ar_1, ar_0 + 1, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 2, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
10.68/4.73	
10.68/4.73			(Comp: ?, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d10(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d9(ar_0, ar_1, ar_2, ar_3))
10.68/4.73	
10.68/4.73			(Comp: 1, Cost: 1)    evalrandom2d7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d8(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2d6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d7(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2d5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d6(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2d4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d5(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2d3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d4(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2d2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d3(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d2(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2d0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d1(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d0(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)    evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
10.68/4.74	
10.68/4.74		start location:	koat_start
10.68/4.74	
10.68/4.74		leaf cost:	0
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	A polynomial rank function with
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb7in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb1in) = -V_1 + V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb6in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb5in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dNewDefaultin) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb4in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dLeafBlock5in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dLeafBlock3in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dLeafBlock1in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dLeafBlockin) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dNodeBlock7in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dNodeBlockin) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dNodeBlock9in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb3in) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2d13) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2d12) = V_2 - V_3
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb8in) = -V_1 + V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2dstop) = -V_1 + V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb2in) = -V_1 + V_2 - 1
10.68/4.74	
10.68/4.74		Pol(evalrandom2d10) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d9) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d8) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d7) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d6) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d5) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d4) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d3) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d2) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d1) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2d0) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2dbb0in) = V_2
10.68/4.74	
10.68/4.74		Pol(evalrandom2dstart) = V_2
10.68/4.74	
10.68/4.74		Pol(koat_start) = V_2
10.68/4.74	
10.68/4.74	orients all transitions weakly and the transition
10.68/4.74	
10.68/4.74		evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
10.68/4.74	
10.68/4.74	strictly and produces the following problem:
10.68/4.74	
10.68/4.74	5:	T:
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ 3 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2d12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d13(ar_0, ar_1, ar_2, e))
10.68/4.74	
10.68/4.74			(Comp: 2, Cost: 1)       evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ?, Cost: 1)       evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d12(ar_0, ar_1, ar_0 + 1, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 2, Cost: 1)       evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)    evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d10(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d9(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d8(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d7(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d6(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d5(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d4(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d3(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d2(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2d0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d1(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d0(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)       evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
10.68/4.74	
10.68/4.74		start location:	koat_start
10.68/4.74	
10.68/4.74		leaf cost:	0
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Repeatedly propagating knowledge in problem 5 produces the following problem:
10.68/4.74	
10.68/4.74	6:	T:
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 4*ar_1, Cost: 1)    evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 3 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 2 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 1 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 = 0 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock3in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlock1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dLeafBlockin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock7in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 2 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlockin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dNodeBlock9in(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ ar_3 >= 4 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2d13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ 3 >= ar_3 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2d12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d13(ar_0, ar_1, ar_2, e))
10.68/4.74	
10.68/4.74			(Comp: 2, Cost: 1)         evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstop(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d12(ar_0, ar_1, ar_0 + 1, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 2, Cost: 1)         evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb8in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
10.68/4.74	
10.68/4.74			(Comp: ar_1, Cost: 1)      evalrandom2dbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb1in(0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d10(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d9(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d8(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d7(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d6(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d5(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d4(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d3(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d2(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2d0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d1(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d0(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 1)         evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3))
10.68/4.74	
10.68/4.74			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
10.68/4.74	
10.68/4.74		start location:	koat_start
10.68/4.74	
10.68/4.74		leaf cost:	0
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Complexity upper bound 29*ar_1 + 17
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Time: 0.495 sec (SMT: 0.374 sec)
10.68/4.74	
10.68/4.74	
10.68/4.74	----------------------------------------
10.68/4.74	
10.68/4.74	(2)
10.68/4.74	BOUNDS(1, n^1)
10.68/4.74	
10.68/4.74	----------------------------------------
10.68/4.74	
10.68/4.74	(3) Loat Proof (FINISHED)
10.68/4.74	
10.68/4.74	
10.68/4.74	### Pre-processing the ITS problem ###
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Initial linear ITS problem
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	      0: evalrandom2dstart -> evalrandom2dbb0in : [], cost: 1
10.68/4.74	
10.68/4.74	      1: evalrandom2dbb0in -> evalrandom2d0 : [], cost: 1
10.68/4.74	
10.68/4.74	      2: evalrandom2d0 -> evalrandom2d1 : [], cost: 1
10.68/4.74	
10.68/4.74	      3: evalrandom2d1 -> evalrandom2d2 : [], cost: 1
10.68/4.74	
10.68/4.74	      4: evalrandom2d2 -> evalrandom2d3 : [], cost: 1
10.68/4.74	
10.68/4.74	      5: evalrandom2d3 -> evalrandom2d4 : [], cost: 1
10.68/4.74	
10.68/4.74	      6: evalrandom2d4 -> evalrandom2d5 : [], cost: 1
10.68/4.74	
10.68/4.74	      7: evalrandom2d5 -> evalrandom2d6 : [], cost: 1
10.68/4.74	
10.68/4.74	      8: evalrandom2d6 -> evalrandom2d7 : [], cost: 1
10.68/4.74	
10.68/4.74	      9: evalrandom2d7 -> evalrandom2d8 : [], cost: 1
10.68/4.74	
10.68/4.74	     10: evalrandom2d8 -> evalrandom2d9 : [], cost: 1
10.68/4.74	
10.68/4.74	     11: evalrandom2d9 -> evalrandom2d10 : [], cost: 1
10.68/4.74	
10.68/4.74	     12: evalrandom2d10 -> evalrandom2dbb1in : A'=0, [], cost: 1
10.68/4.74	
10.68/4.74	     13: evalrandom2dbb1in -> evalrandom2dbb2in : [ B>=1+A ], cost: 1
10.68/4.74	
10.68/4.74	     14: evalrandom2dbb1in -> evalrandom2dbb8in : [ A>=B ], cost: 1
10.68/4.74	
10.68/4.74	     15: evalrandom2dbb2in -> evalrandom2d12 : C'=1+A, [], cost: 1
10.68/4.74	
10.68/4.74	     16: evalrandom2d12 -> evalrandom2d13 : D'=free, [], cost: 1
10.68/4.74	
10.68/4.74	     17: evalrandom2d13 -> evalrandom2dbb3in : [ D>=0 && 3>=D ], cost: 1
10.68/4.74	
10.68/4.74	     18: evalrandom2d13 -> evalrandom2dbb1in : A'=C, [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     19: evalrandom2d13 -> evalrandom2dbb1in : A'=C, [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     20: evalrandom2dbb3in -> evalrandom2dNodeBlock9in : [], cost: 1
10.68/4.74	
10.68/4.74	     21: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlockin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     22: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlock7in : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     23: evalrandom2dNodeBlockin -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     24: evalrandom2dNodeBlockin -> evalrandom2dLeafBlock1in : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     25: evalrandom2dLeafBlockin -> evalrandom2dbb4in : [ D==0 ], cost: 1
10.68/4.74	
10.68/4.74	     26: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     27: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     28: evalrandom2dbb4in -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     29: evalrandom2dLeafBlock1in -> evalrandom2dbb5in : [ D==1 ], cost: 1
10.68/4.74	
10.68/4.74	     30: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     31: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     32: evalrandom2dbb5in -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     33: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock3in : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     34: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     35: evalrandom2dLeafBlock3in -> evalrandom2dbb6in : [ D==2 ], cost: 1
10.68/4.74	
10.68/4.74	     36: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     37: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     38: evalrandom2dbb6in -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     39: evalrandom2dLeafBlock5in -> evalrandom2dbb7in : [ D==3 ], cost: 1
10.68/4.74	
10.68/4.74	     40: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     41: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     42: evalrandom2dbb7in -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     43: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     44: evalrandom2dbb8in -> evalrandom2dstop : [], cost: 1
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Removed unreachable and leaf rules:
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	      0: evalrandom2dstart -> evalrandom2dbb0in : [], cost: 1
10.68/4.74	
10.68/4.74	      1: evalrandom2dbb0in -> evalrandom2d0 : [], cost: 1
10.68/4.74	
10.68/4.74	      2: evalrandom2d0 -> evalrandom2d1 : [], cost: 1
10.68/4.74	
10.68/4.74	      3: evalrandom2d1 -> evalrandom2d2 : [], cost: 1
10.68/4.74	
10.68/4.74	      4: evalrandom2d2 -> evalrandom2d3 : [], cost: 1
10.68/4.74	
10.68/4.74	      5: evalrandom2d3 -> evalrandom2d4 : [], cost: 1
10.68/4.74	
10.68/4.74	      6: evalrandom2d4 -> evalrandom2d5 : [], cost: 1
10.68/4.74	
10.68/4.74	      7: evalrandom2d5 -> evalrandom2d6 : [], cost: 1
10.68/4.74	
10.68/4.74	      8: evalrandom2d6 -> evalrandom2d7 : [], cost: 1
10.68/4.74	
10.68/4.74	      9: evalrandom2d7 -> evalrandom2d8 : [], cost: 1
10.68/4.74	
10.68/4.74	     10: evalrandom2d8 -> evalrandom2d9 : [], cost: 1
10.68/4.74	
10.68/4.74	     11: evalrandom2d9 -> evalrandom2d10 : [], cost: 1
10.68/4.74	
10.68/4.74	     12: evalrandom2d10 -> evalrandom2dbb1in : A'=0, [], cost: 1
10.68/4.74	
10.68/4.74	     13: evalrandom2dbb1in -> evalrandom2dbb2in : [ B>=1+A ], cost: 1
10.68/4.74	
10.68/4.74	     15: evalrandom2dbb2in -> evalrandom2d12 : C'=1+A, [], cost: 1
10.68/4.74	
10.68/4.74	     16: evalrandom2d12 -> evalrandom2d13 : D'=free, [], cost: 1
10.68/4.74	
10.68/4.74	     17: evalrandom2d13 -> evalrandom2dbb3in : [ D>=0 && 3>=D ], cost: 1
10.68/4.74	
10.68/4.74	     18: evalrandom2d13 -> evalrandom2dbb1in : A'=C, [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     19: evalrandom2d13 -> evalrandom2dbb1in : A'=C, [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     20: evalrandom2dbb3in -> evalrandom2dNodeBlock9in : [], cost: 1
10.68/4.74	
10.68/4.74	     21: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlockin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     22: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlock7in : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     23: evalrandom2dNodeBlockin -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     24: evalrandom2dNodeBlockin -> evalrandom2dLeafBlock1in : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     25: evalrandom2dLeafBlockin -> evalrandom2dbb4in : [ D==0 ], cost: 1
10.68/4.74	
10.68/4.74	     26: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     27: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     28: evalrandom2dbb4in -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     29: evalrandom2dLeafBlock1in -> evalrandom2dbb5in : [ D==1 ], cost: 1
10.68/4.74	
10.68/4.74	     30: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     31: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     32: evalrandom2dbb5in -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     33: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock3in : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     34: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     35: evalrandom2dLeafBlock3in -> evalrandom2dbb6in : [ D==2 ], cost: 1
10.68/4.74	
10.68/4.74	     36: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     37: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     38: evalrandom2dbb6in -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     39: evalrandom2dLeafBlock5in -> evalrandom2dbb7in : [ D==3 ], cost: 1
10.68/4.74	
10.68/4.74	     40: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     41: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     42: evalrandom2dbb7in -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     43: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	### Simplification by acceleration and chaining ###
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Eliminated locations (on linear paths):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     58: evalrandom2dbb1in -> evalrandom2d13 : C'=1+A, D'=free, [ B>=1+A ], cost: 3
10.68/4.74	
10.68/4.74	     18: evalrandom2d13 -> evalrandom2dbb1in : A'=C, [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     19: evalrandom2d13 -> evalrandom2dbb1in : A'=C, [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     59: evalrandom2d13 -> evalrandom2dNodeBlock9in : [ D>=0 && 3>=D ], cost: 2
10.68/4.74	
10.68/4.74	     21: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlockin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     22: evalrandom2dNodeBlock9in -> evalrandom2dNodeBlock7in : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     23: evalrandom2dNodeBlockin -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     24: evalrandom2dNodeBlockin -> evalrandom2dLeafBlock1in : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     26: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     27: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     60: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=C, [ D==0 ], cost: 2
10.68/4.74	
10.68/4.74	     30: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     31: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     61: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=C, [ D==1 ], cost: 2
10.68/4.74	
10.68/4.74	     33: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock3in : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     34: evalrandom2dNodeBlock7in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     36: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     37: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     62: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=C, [ D==2 ], cost: 2
10.68/4.74	
10.68/4.74	     40: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     41: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     63: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=C, [ D==3 ], cost: 2
10.68/4.74	
10.68/4.74	     43: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Eliminated locations (on tree-shaped paths):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     64: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && 0>=1+free ], cost: 4
10.68/4.74	
10.68/4.74	     65: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free>=4 ], cost: 4
10.68/4.74	
10.68/4.74	     66: evalrandom2dbb1in -> evalrandom2dNodeBlock9in : C'=1+A, D'=free, [ B>=1+A && free>=0 && 3>=free ], cost: 5
10.68/4.74	
10.68/4.74	     67: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 2
10.68/4.74	
10.68/4.74	     68: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock1in : [ 1>=D && D>=1 ], cost: 2
10.68/4.74	
10.68/4.74	     69: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock3in : [ D>=2 && 2>=D ], cost: 2
10.68/4.74	
10.68/4.74	     70: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 2
10.68/4.74	
10.68/4.74	     26: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     27: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     60: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=C, [ D==0 ], cost: 2
10.68/4.74	
10.68/4.74	     30: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     31: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     61: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=C, [ D==1 ], cost: 2
10.68/4.74	
10.68/4.74	     36: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     37: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     62: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=C, [ D==2 ], cost: 2
10.68/4.74	
10.68/4.74	     40: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     41: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     63: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=C, [ D==3 ], cost: 2
10.68/4.74	
10.68/4.74	     43: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Accelerating simple loops of location 13.
10.68/4.74	
10.68/4.74	   Accelerating the following rules:
10.68/4.74	
10.68/4.74	     64: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && 0>=1+free ], cost: 4
10.68/4.74	
10.68/4.74	     65: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free>=4 ], cost: 4
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	   Accelerated rule 64 with metering function -A+B, yielding the new rule 71.
10.68/4.74	
10.68/4.74	   Accelerated rule 65 with metering function -A+B, yielding the new rule 72.
10.68/4.74	
10.68/4.74	   Removing the simple loops: 64 65.
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Accelerated all simple loops using metering functions (where possible):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     66: evalrandom2dbb1in -> evalrandom2dNodeBlock9in : C'=1+A, D'=free, [ B>=1+A && free>=0 && 3>=free ], cost: 5
10.68/4.74	
10.68/4.74	     71: evalrandom2dbb1in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1+A && 0>=1+free ], cost: -4*A+4*B
10.68/4.74	
10.68/4.74	     72: evalrandom2dbb1in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1+A && free>=4 ], cost: -4*A+4*B
10.68/4.74	
10.68/4.74	     67: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 2
10.68/4.74	
10.68/4.74	     68: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock1in : [ 1>=D && D>=1 ], cost: 2
10.68/4.74	
10.68/4.74	     69: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock3in : [ D>=2 && 2>=D ], cost: 2
10.68/4.74	
10.68/4.74	     70: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 2
10.68/4.74	
10.68/4.74	     26: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     27: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     60: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=C, [ D==0 ], cost: 2
10.68/4.74	
10.68/4.74	     30: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     31: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     61: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=C, [ D==1 ], cost: 2
10.68/4.74	
10.68/4.74	     36: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     37: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     62: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=C, [ D==2 ], cost: 2
10.68/4.74	
10.68/4.74	     40: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     41: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     63: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=C, [ D==3 ], cost: 2
10.68/4.74	
10.68/4.74	     43: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Chained accelerated rules (with incoming rules):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     74: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && 0>=1+free ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     80: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && free>=4 ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     66: evalrandom2dbb1in -> evalrandom2dNodeBlock9in : C'=1+A, D'=free, [ B>=1+A && free>=0 && 3>=free ], cost: 5
10.68/4.74	
10.68/4.74	     67: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlockin : [ 0>=D ], cost: 2
10.68/4.74	
10.68/4.74	     68: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock1in : [ 1>=D && D>=1 ], cost: 2
10.68/4.74	
10.68/4.74	     69: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock3in : [ D>=2 && 2>=D ], cost: 2
10.68/4.74	
10.68/4.74	     70: evalrandom2dNodeBlock9in -> evalrandom2dLeafBlock5in : [ D>=3 ], cost: 2
10.68/4.74	
10.68/4.74	     26: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     27: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     60: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=C, [ D==0 ], cost: 2
10.68/4.74	
10.68/4.74	     75: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==0 && B>=1+C && 0>=1+free ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     81: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==0 && B>=1+C && free>=4 ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     30: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     31: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     61: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=C, [ D==1 ], cost: 2
10.68/4.74	
10.68/4.74	     76: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==1 && B>=1+C && 0>=1+free ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     82: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==1 && B>=1+C && free>=4 ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     36: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     37: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     62: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=C, [ D==2 ], cost: 2
10.68/4.74	
10.68/4.74	     77: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==2 && B>=1+C && 0>=1+free ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     83: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==2 && B>=1+C && free>=4 ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     40: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     41: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     63: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=C, [ D==3 ], cost: 2
10.68/4.74	
10.68/4.74	     78: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==3 && B>=1+C && 0>=1+free ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     84: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==3 && B>=1+C && free>=4 ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     43: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     73: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1+C && 0>=1+free ], cost: 1-4*C+4*B
10.68/4.74	
10.68/4.74	     79: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1+C && free>=4 ], cost: 1-4*C+4*B
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Eliminated locations (on tree-shaped paths):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     74: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && 0>=1+free ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     80: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && free>=4 ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     85: evalrandom2dbb1in -> evalrandom2dLeafBlockin : C'=1+A, D'=free, [ B>=1+A && free>=0 && 0>=free ], cost: 7
10.68/4.74	
10.68/4.74	     86: evalrandom2dbb1in -> evalrandom2dLeafBlock1in : C'=1+A, D'=free, [ B>=1+A && 1>=free && free>=1 ], cost: 7
10.68/4.74	
10.68/4.74	     87: evalrandom2dbb1in -> evalrandom2dLeafBlock3in : C'=1+A, D'=free, [ B>=1+A && free>=2 && 2>=free ], cost: 7
10.68/4.74	
10.68/4.74	     88: evalrandom2dbb1in -> evalrandom2dLeafBlock5in : C'=1+A, D'=free, [ B>=1+A && 3>=free && free>=3 ], cost: 7
10.68/4.74	
10.68/4.74	     26: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ 0>=1+D ], cost: 1
10.68/4.74	
10.68/4.74	     27: evalrandom2dLeafBlockin -> evalrandom2dNewDefaultin : [ D>=1 ], cost: 1
10.68/4.74	
10.68/4.74	     60: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=C, [ D==0 ], cost: 2
10.68/4.74	
10.68/4.74	     75: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==0 && B>=1+C && 0>=1+free ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     81: evalrandom2dLeafBlockin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==0 && B>=1+C && free>=4 ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     30: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ 0>=D ], cost: 1
10.68/4.74	
10.68/4.74	     31: evalrandom2dLeafBlock1in -> evalrandom2dNewDefaultin : [ D>=2 ], cost: 1
10.68/4.74	
10.68/4.74	     61: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=C, [ D==1 ], cost: 2
10.68/4.74	
10.68/4.74	     76: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==1 && B>=1+C && 0>=1+free ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     82: evalrandom2dLeafBlock1in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==1 && B>=1+C && free>=4 ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     36: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ 1>=D ], cost: 1
10.68/4.74	
10.68/4.74	     37: evalrandom2dLeafBlock3in -> evalrandom2dNewDefaultin : [ D>=3 ], cost: 1
10.68/4.74	
10.68/4.74	     62: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=C, [ D==2 ], cost: 2
10.68/4.74	
10.68/4.74	     77: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==2 && B>=1+C && 0>=1+free ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     83: evalrandom2dLeafBlock3in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==2 && B>=1+C && free>=4 ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     40: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ 2>=D ], cost: 1
10.68/4.74	
10.68/4.74	     41: evalrandom2dLeafBlock5in -> evalrandom2dNewDefaultin : [ D>=4 ], cost: 1
10.68/4.74	
10.68/4.74	     63: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=C, [ D==3 ], cost: 2
10.68/4.74	
10.68/4.74	     78: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==3 && B>=1+C && 0>=1+free ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     84: evalrandom2dLeafBlock5in -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ D==3 && B>=1+C && free>=4 ], cost: 2-4*C+4*B
10.68/4.74	
10.68/4.74	     43: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     73: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1+C && 0>=1+free ], cost: 1-4*C+4*B
10.68/4.74	
10.68/4.74	     79: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1+C && free>=4 ], cost: 1-4*C+4*B
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Eliminated locations (on tree-shaped paths):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     74: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && 0>=1+free ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     80: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && free>=4 ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     89: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==0 ], cost: 9
10.68/4.74	
10.68/4.74	     90: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==1 ], cost: 9
10.68/4.74	
10.68/4.74	     91: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==2 ], cost: 9
10.68/4.74	
10.68/4.74	     92: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==3 ], cost: 9
10.68/4.74	
10.68/4.74	     43: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=C, [], cost: 1
10.68/4.74	
10.68/4.74	     73: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1+C && 0>=1+free ], cost: 1-4*C+4*B
10.68/4.74	
10.68/4.74	     79: evalrandom2dNewDefaultin -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1+C && free>=4 ], cost: 1-4*C+4*B
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Applied pruning (of leafs and parallel rules):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     74: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && 0>=1+free ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     80: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && free>=4 ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     89: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==0 ], cost: 9
10.68/4.74	
10.68/4.74	     90: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==1 ], cost: 9
10.68/4.74	
10.68/4.74	     91: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==2 ], cost: 9
10.68/4.74	
10.68/4.74	     92: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=free, [ B>=1+A && free==3 ], cost: 9
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Accelerating simple loops of location 13.
10.68/4.74	
10.68/4.74	   Simplified some of the simple loops (and removed duplicate rules).
10.68/4.74	
10.68/4.74	   Accelerating the following rules:
10.68/4.74	
10.68/4.74	     89: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=0, [ B>=1+A ], cost: 9
10.68/4.74	
10.68/4.74	     90: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=1, [ B>=1+A ], cost: 9
10.68/4.74	
10.68/4.74	     91: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=2, [ B>=1+A ], cost: 9
10.68/4.74	
10.68/4.74	     92: evalrandom2dbb1in -> evalrandom2dbb1in : A'=1+A, C'=1+A, D'=3, [ B>=1+A ], cost: 9
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	   Accelerated rule 89 with metering function -A+B, yielding the new rule 93.
10.68/4.74	
10.68/4.74	   Accelerated rule 90 with metering function -A+B, yielding the new rule 94.
10.68/4.74	
10.68/4.74	   Accelerated rule 91 with metering function -A+B, yielding the new rule 95.
10.68/4.74	
10.68/4.74	   Accelerated rule 92 with metering function -A+B, yielding the new rule 96.
10.68/4.74	
10.68/4.74	   Removing the simple loops: 89 90 91 92.
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Accelerated all simple loops using metering functions (where possible):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     74: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && 0>=1+free ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     80: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && free>=4 ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     93: evalrandom2dbb1in -> evalrandom2dbb1in : A'=B, C'=B, D'=0, [ B>=1+A ], cost: -9*A+9*B
10.68/4.74	
10.68/4.74	     94: evalrandom2dbb1in -> evalrandom2dbb1in : A'=B, C'=B, D'=1, [ B>=1+A ], cost: -9*A+9*B
10.68/4.74	
10.68/4.74	     95: evalrandom2dbb1in -> evalrandom2dbb1in : A'=B, C'=B, D'=2, [ B>=1+A ], cost: -9*A+9*B
10.68/4.74	
10.68/4.74	     96: evalrandom2dbb1in -> evalrandom2dbb1in : A'=B, C'=B, D'=3, [ B>=1+A ], cost: -9*A+9*B
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Chained accelerated rules (with incoming rules):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     56: evalrandom2dstart -> evalrandom2dbb1in : A'=0, [], cost: 13
10.68/4.74	
10.68/4.74	     74: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && 0>=1+free ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     80: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && free>=4 ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     97: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=0, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	     98: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=1, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	     99: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=2, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	    100: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=3, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Removed unreachable locations (and leaf rules with constant cost):
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     74: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && 0>=1+free ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     80: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && free>=4 ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     97: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=0, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	     98: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=1, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	     99: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=2, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	    100: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=3, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	### Computing asymptotic complexity ###
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Fully simplified ITS problem
10.68/4.74	
10.68/4.74	   Start location: evalrandom2dstart
10.68/4.74	
10.68/4.74	     74: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && 0>=1+free ], cost: 13+4*B
10.68/4.74	
10.68/4.74	     80: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=free, [ B>=1 && free>=4 ], cost: 13+4*B
10.68/4.74	
10.68/4.74	    100: evalrandom2dstart -> evalrandom2dbb1in : A'=B, C'=B, D'=3, [ B>=1 ], cost: 13+9*B
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Computing asymptotic complexity for rule 74
10.68/4.74	
10.68/4.74	   Solved the limit problem by the following transformations:
10.68/4.74	
10.68/4.74	      Created initial limit problem:
10.68/4.74	
10.68/4.74	      13+4*B (+), B (+/+!), -free (+/+!) [not solved]
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	      removing all constraints (solved by SMT)
10.68/4.74	
10.68/4.74	      resulting limit problem: [solved]
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	      applying transformation rule (C) using substitution {free==-n,B==n}
10.68/4.74	
10.68/4.74	      resulting limit problem:
10.68/4.74	
10.68/4.74	      [solved]
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	   Solution:
10.68/4.74	
10.68/4.74	      free / -n
10.68/4.74	
10.68/4.74	      B / n
10.68/4.74	
10.68/4.74	   Resulting cost 13+4*n has complexity: Poly(n^1)
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Found new complexity Poly(n^1).
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	Obtained the following overall complexity (w.r.t. the length of the input n):
10.68/4.74	
10.68/4.74	   Complexity:  Poly(n^1)
10.68/4.74	
10.68/4.74	   Cpx degree:  1
10.68/4.74	
10.68/4.74	   Solved cost: 13+4*n
10.68/4.74	
10.68/4.74	   Rule cost:   13+4*B
10.68/4.74	
10.68/4.74	   Rule guard:  [ B>=1 && 0>=1+free ]
10.68/4.74	
10.68/4.74	
10.68/4.74	
10.68/4.74	WORST_CASE(Omega(n^1),?)
10.68/4.74	
10.68/4.74	
10.68/4.74	----------------------------------------
10.68/4.74	
10.68/4.74	(4)
10.68/4.74	BOUNDS(n^1, INF)
10.68/4.77	EOF