2.10/1.68	WORST_CASE(?, O(n^1))
2.10/1.69	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.10/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.10/1.69	
2.10/1.69	
2.10/1.69	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.10/1.69	
2.10/1.69	(0) CpxIntTrs
2.10/1.69	(1) Koat Proof [FINISHED, 477 ms]
2.10/1.69	(2) BOUNDS(1, n^1)
2.10/1.69	
2.10/1.69	
2.10/1.69	----------------------------------------
2.10/1.69	
2.10/1.69	(0)
2.10/1.69	Obligation:
2.10/1.69	Complexity Int TRS consisting of the following rules:
2.10/1.69	eval_render_ht_start(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb0_in(v_.0, v_0, v_level, v_old_level)) :|: TRUE
2.10/1.69	eval_render_ht_bb0_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb1_in(v_old_level, v_0, v_level, v_old_level)) :|: TRUE
2.10/1.69	eval_render_ht_bb1_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_LeafBlock_in(v_.0, v_level - v_.0, v_level, v_old_level)) :|: TRUE
2.10/1.69	eval_render_ht_LeafBlock_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb2_in(v_.0, v_0, v_level, v_old_level)) :|: v_0 + 7 <= 14
2.10/1.69	eval_render_ht_LeafBlock_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_NewDefault_in(v_.0, v_0, v_level, v_old_level)) :|: v_0 + 7 > 14
2.10/1.69	eval_render_ht_bb2_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_stop(v_.0, v_0, v_level, v_old_level)) :|: TRUE
2.10/1.69	eval_render_ht_NewDefault_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb3_in(v_.0, v_0, v_level, v_old_level)) :|: TRUE
2.10/1.69	eval_render_ht_bb3_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb1_in(v_.0 + 4, v_0, v_level, v_old_level)) :|: v_level > v_.0
2.10/1.69	eval_render_ht_bb3_in(v_.0, v_0, v_level, v_old_level) -> Com_1(eval_render_ht_bb1_in(v_.0 - 4, v_0, v_level, v_old_level)) :|: v_level <= v_.0
2.10/1.69	
2.10/1.69	The start-symbols are:[eval_render_ht_start_4]
2.10/1.69	
2.10/1.69	
2.10/1.69	----------------------------------------
2.10/1.69	
2.10/1.69	(1) Koat Proof (FINISHED)
2.10/1.69	YES(?, 6*ar_1 + 6*ar_3 + 11)
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	Initial complexity problem:
2.10/1.69	
2.10/1.69	1:	T:
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.10/1.69	
2.10/1.69	2:	T:
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	A polynomial rank function with
2.10/1.69	
2.10/1.69		Pol(evalrenderhtstart) = 2
2.10/1.69	
2.10/1.69		Pol(evalrenderhtbb0in) = 2
2.10/1.69	
2.10/1.69		Pol(evalrenderhtbb1in) = 2
2.10/1.69	
2.10/1.69		Pol(evalrenderhtLeafBlockin) = 2
2.10/1.69	
2.10/1.69		Pol(evalrenderhtbb2in) = 1
2.10/1.69	
2.10/1.69		Pol(evalrenderhtNewDefaultin) = 2
2.10/1.69	
2.10/1.69		Pol(evalrenderhtstop) = 0
2.10/1.69	
2.10/1.69		Pol(evalrenderhtbb3in) = 2
2.10/1.69	
2.10/1.69		Pol(koat_start) = 2
2.10/1.69	
2.10/1.69	orients all transitions weakly and the transitions
2.10/1.69	
2.10/1.69		evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69		evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69	strictly and produces the following problem:
2.10/1.69	
2.10/1.69	3:	T:
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.10/1.69	
2.10/1.69	  For symbol evalrenderhtNewDefaultin: X_3 - 8 >= 0
2.10/1.69	
2.10/1.69	  For symbol evalrenderhtbb2in: -X_3 + 7 >= 0
2.10/1.69	
2.10/1.69	  For symbol evalrenderhtbb3in: X_3 - 8 >= 0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	This yielded the following problem:
2.10/1.69	
2.10/1.69	4:	T:
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
2.10/1.69	
2.10/1.69		koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69	We thus obtain the following problem:
2.10/1.69	
2.10/1.69	5:	T:
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	Testing for reachability in the complexity graph removes the following transition from problem 5:
2.10/1.69	
2.10/1.69		evalrenderhtstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69	We thus obtain the following problem:
2.10/1.69	
2.10/1.69	6:	T:
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	By chaining the transition evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 + 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ] with all transitions in problem 6, the following new transition is obtained:
2.10/1.69	
2.10/1.69		evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69	We thus obtain the following problem:
2.10/1.69	
2.10/1.69	7:	T:
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 2)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	By chaining the transition evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_0 - 4, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ] with all transitions in problem 7, the following new transition is obtained:
2.10/1.69	
2.10/1.69		evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69	We thus obtain the following problem:
2.10/1.69	
2.10/1.69	8:	T:
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 2)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 2)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	Repeatedly propagating knowledge in problem 8 produces the following problem:
2.10/1.69	
2.10/1.69	9:	T:
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 2)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 2)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	A polynomial rank function with
2.10/1.69	
2.10/1.69		Pol(evalrenderhtNewDefaultin) = -V_1 + V_4
2.10/1.69	
2.10/1.69		Pol(evalrenderhtbb3in) = -V_1 + V_4
2.10/1.69	
2.10/1.69		Pol(evalrenderhtLeafBlockin) = -V_1 + V_4
2.10/1.69	
2.10/1.69	and size complexities
2.10/1.69	
2.10/1.69		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.10/1.69	
2.10/1.69		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.10/1.69	
2.10/1.69		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.10/1.69	
2.10/1.69		S("evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))", 0-0) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))", 0-2) = ar_1 + ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))", 0-3) = ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]", 0-0) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]", 0-2) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]", 0-3) = ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]", 0-0) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]", 0-2) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]", 0-3) = ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]", 0-0) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]", 0-2) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]", 0-3) = ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]", 0-0) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]", 0-2) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]", 0-3) = ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = ar_3
2.10/1.69	
2.10/1.69		S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_0 >= ar_3 ]", 0-0) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_0 >= ar_3 ]", 0-1) = ar_1
2.10/1.69	
2.10/1.69		S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_0 >= ar_3 ]", 0-2) = ?
2.10/1.69	
2.10/1.69		S("evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\\ ar_0 >= ar_3 ]", 0-3) = ar_3
2.10/1.69	
2.10/1.69	orients the transitions
2.10/1.69	
2.10/1.69		evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69		evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69		evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69	weakly and the transition
2.10/1.69	
2.10/1.69		evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69	strictly and produces the following problem:
2.10/1.69	
2.10/1.69	10:	T:
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 2)              evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: ar_1 + ar_3, Cost: 2)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)              evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)              evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)              evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ?, Cost: 1)              evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)              evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)              evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)              koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	Repeatedly propagating knowledge in problem 10 produces the following problem:
2.10/1.69	
2.10/1.69	11:	T:
2.10/1.69	
2.10/1.69			(Comp: ar_1 + ar_3 + 1, Cost: 2)    evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 - 4, ar_1, ar_3 - ar_0 + 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_0 >= ar_3 ]
2.10/1.69	
2.10/1.69			(Comp: ar_1 + ar_3, Cost: 2)        evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0 + 4, ar_1, ar_3 - ar_0 - 4, ar_3)) [ ar_2 - 8 >= 0 /\ ar_3 >= ar_0 + 1 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)                  evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + 7 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 8 >= 0 ]
2.10/1.69	
2.10/1.69			(Comp: 2, Cost: 1)                  evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb2in(ar_0, ar_1, ar_2, ar_3)) [ 7 >= ar_2 ]
2.10/1.69	
2.10/1.69			(Comp: ar_1 + ar_3 + 1, Cost: 1)    evalrenderhtLeafBlockin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtNewDefaultin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 8 ]
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)                  evalrenderhtbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtLeafBlockin(ar_0, ar_1, ar_3 - ar_0, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)                  evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb1in(ar_1, ar_1, ar_2, ar_3))
2.10/1.69	
2.10/1.69			(Comp: 1, Cost: 1)                  koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrenderhtbb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.10/1.69	
2.10/1.69		start location:	koat_start
2.10/1.69	
2.10/1.69		leaf cost:	0
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	Complexity upper bound 6*ar_1 + 6*ar_3 + 11
2.10/1.69	
2.10/1.69	
2.10/1.69	
2.10/1.69	Time: 0.473 sec (SMT: 0.401 sec)
2.10/1.69	
2.10/1.69	
2.10/1.69	----------------------------------------
2.10/1.69	
2.10/1.69	(2)
2.10/1.69	BOUNDS(1, n^1)
2.63/1.71	EOF