2.81/1.83	WORST_CASE(?, O(n^1))
2.81/1.84	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.81/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.81/1.84	
2.81/1.84	
2.81/1.84	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.81/1.84	
2.81/1.84	(0) CpxIntTrs
2.81/1.84	(1) Koat Proof [FINISHED, 578 ms]
2.81/1.84	(2) BOUNDS(1, n^1)
2.81/1.84	
2.81/1.84	
2.81/1.84	----------------------------------------
2.81/1.84	
2.81/1.84	(0)
2.81/1.84	Obligation:
2.81/1.84	Complexity Int TRS consisting of the following rules:
2.81/1.84	eval_Loopus2011_ex3_start(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb0_in(v_.0, v_b, v_x)) :|: TRUE
2.81/1.84	eval_Loopus2011_ex3_bb0_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb1_in(v_x, v_b, v_x)) :|: TRUE
2.81/1.84	eval_Loopus2011_ex3_bb1_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb2_in(v_.0, v_b, v_x)) :|: 0 < v_.0 && v_.0 < 255
2.81/1.84	eval_Loopus2011_ex3_bb1_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb3_in(v_.0, v_b, v_x)) :|: 0 >= v_.0
2.81/1.84	eval_Loopus2011_ex3_bb1_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb3_in(v_.0, v_b, v_x)) :|: v_.0 >= 255
2.81/1.84	eval_Loopus2011_ex3_bb2_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb1_in(v_.0 + 1, v_b, v_x)) :|: v_b < 0
2.81/1.84	eval_Loopus2011_ex3_bb2_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb1_in(v_.0 + 1, v_b, v_x)) :|: v_b > 0
2.81/1.84	eval_Loopus2011_ex3_bb2_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_bb1_in(v_.0 - 1, v_b, v_x)) :|: v_b >= 0 && v_b <= 0
2.81/1.84	eval_Loopus2011_ex3_bb3_in(v_.0, v_b, v_x) -> Com_1(eval_Loopus2011_ex3_stop(v_.0, v_b, v_x)) :|: TRUE
2.81/1.84	
2.81/1.84	The start-symbols are:[eval_Loopus2011_ex3_start_3]
2.81/1.84	
2.81/1.84	
2.81/1.84	----------------------------------------
2.81/1.84	
2.81/1.84	(1) Koat Proof (FINISHED)
2.81/1.84	YES(?, 4076*ar_1 + 16)
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	Initial complexity problem:
2.81/1.84	
2.81/1.84	1:	T:
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.81/1.84	
2.81/1.84	2:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	A polynomial rank function with
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3start) = 2
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb0in) = 2
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb1in) = 2
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb2in) = 2
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb3in) = 1
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3stop) = 0
2.81/1.84	
2.81/1.84		Pol(koat_start) = 2
2.81/1.84	
2.81/1.84	orients all transitions weakly and the transitions
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84	strictly and produces the following problem:
2.81/1.84	
2.81/1.84	3:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.81/1.84	
2.81/1.84	  For symbol evalLoopus2011ex3bb2in: -X_1 + 254 >= 0 /\ X_1 - 1 >= 0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	This yielded the following problem:
2.81/1.84	
2.81/1.84	4:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	By chaining the transition koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
2.81/1.84	
2.81/1.84		koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	5:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	Testing for reachability in the complexity graph removes the following transition from problem 5:
2.81/1.84	
2.81/1.84		evalLoopus2011ex3start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	6:	T:
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	By chaining the transition evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] with all transitions in problem 6, the following new transition is obtained:
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	7:	T:
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	By chaining the transition evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ] with all transitions in problem 7, the following new transition is obtained:
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	8:	T:
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 1)    evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	Testing for reachability in the complexity graph removes the following transition from problem 8:
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2))
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	9:	T:
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	By chaining the transition koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ] with all transitions in problem 9, the following new transition is obtained:
2.81/1.84	
2.81/1.84		koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	10:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 1)    evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	Testing for reachability in the complexity graph removes the following transition from problem 10:
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2))
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	11:	T:
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	By chaining the transition evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 ] with all transitions in problem 11, the following new transitions are obtained:
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	12:	T:
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 3)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 2)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	A polynomial rank function with
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb2in) = 1
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3stop) = 0
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb1in) = 1
2.81/1.84	
2.81/1.84		Pol(koat_start) = 1
2.81/1.84	
2.81/1.84	orients all transitions weakly and the transition
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84	strictly and produces the following problem:
2.81/1.84	
2.81/1.84	13:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 3)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 2)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	By chaining the transition evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ] with all transitions in problem 13, the following new transitions are obtained:
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84	We thus obtain the following problem:
2.81/1.84	
2.81/1.84	14:	T:
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 3)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 2)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 3)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 2)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	A polynomial rank function with
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb2in) = 1
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3stop) = 0
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb1in) = 1
2.81/1.84	
2.81/1.84		Pol(koat_start) = 1
2.81/1.84	
2.81/1.84	orients all transitions weakly and the transition
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84	strictly and produces the following problem:
2.81/1.84	
2.81/1.84	15:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 3)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 2)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 3)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 2)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 2)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	A polynomial rank function with
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb2in) = 2*V_1 - 1
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb1in) = 2*V_1
2.81/1.84	
2.81/1.84	and size complexities
2.81/1.84	
2.81/1.84		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_1
2.81/1.84	
2.81/1.84		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\\ 254 >= ar_0 ]", 0-0) = 254
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\\ 254 >= ar_0 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\\ 254 >= ar_0 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-0) = ar_1 + 253
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]", 0-0) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = 0 ]", 0-0) = 253
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = 0 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = 0 ]", 0-2) = 0
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-0) = 254
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 255 ]", 0-0) = 255
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 255 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 255 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-0) = 254
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 255 ]", 0-0) = 255
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 255 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 255 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84	orients the transitions
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84	weakly and the transitions
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84	strictly and produces the following problem:
2.81/1.84	
2.81/1.84	16:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 3)         evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 2)         evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 3)         evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: ?, Cost: 2)         evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: 2*ar_1, Cost: 1)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)         evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)         evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 2*ar_1, Cost: 1)    evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 2)         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	A polynomial rank function with
2.81/1.84	
2.81/1.84		Pol(evalLoopus2011ex3bb2in) = -V_1 + 255
2.81/1.84	
2.81/1.84	and size complexities
2.81/1.84	
2.81/1.84		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_1
2.81/1.84	
2.81/1.84		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\\ 254 >= ar_0 ]", 0-0) = 254
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\\ 254 >= ar_0 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\\ 254 >= ar_0 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-0) = ar_1 + 253
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]", 0-0) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = 0 ]", 0-0) = 253
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = 0 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = 0 ]", 0-2) = 0
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-0) = 254
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 255 ]", 0-0) = 255
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 255 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 + 1 /\\ ar_0 + 1 >= 255 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-0) = 254
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 1 /\\ 254 >= ar_0 + 1 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 255 ]", 0-0) = 255
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 255 ]", 0-1) = ar_1
2.81/1.84	
2.81/1.84		S("evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_0 + 1 >= 255 ]", 0-2) = ar_2
2.81/1.84	
2.81/1.84	orients the transitions
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84	weakly and the transitions
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84		evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84	strictly and produces the following problem:
2.81/1.84	
2.81/1.84	17:	T:
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 3)            evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 1018*ar_1, Cost: 2)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 3)            evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 1018*ar_1, Cost: 2)    evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0 + 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 + 1 /\ ar_0 + 1 >= 1 /\ 254 >= ar_0 + 1 ]
2.81/1.84	
2.81/1.84			(Comp: 2*ar_1, Cost: 1)       evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_0 - 1, ar_1, ar_2)) [ -ar_0 + 254 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = 0 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)            evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ ar_0 >= 255 ]
2.81/1.84	
2.81/1.84			(Comp: 2, Cost: 2)            evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3stop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 2*ar_1, Cost: 1)       evalLoopus2011ex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 /\ 254 >= ar_0 ]
2.81/1.84	
2.81/1.84			(Comp: 1, Cost: 2)            koat_start(ar_0, ar_1, ar_2) -> Com_1(evalLoopus2011ex3bb1in(ar_1, ar_1, ar_2)) [ 0 <= 0 ]
2.81/1.84	
2.81/1.84		start location:	koat_start
2.81/1.84	
2.81/1.84		leaf cost:	0
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	Complexity upper bound 4076*ar_1 + 16
2.81/1.84	
2.81/1.84	
2.81/1.84	
2.81/1.84	Time: 0.527 sec (SMT: 0.449 sec)
2.81/1.84	
2.81/1.84	
2.81/1.84	----------------------------------------
2.81/1.84	
2.81/1.84	(2)
2.81/1.84	BOUNDS(1, n^1)
2.81/1.86	EOF