2.46/1.65	WORST_CASE(?, O(1))
2.46/1.66	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.46/1.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.46/1.66	
2.46/1.66	
2.46/1.66	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
2.46/1.66	
2.46/1.66	(0) CpxIntTrs
2.46/1.66	(1) Koat Proof [FINISHED, 378 ms]
2.46/1.66	(2) BOUNDS(1, 1)
2.46/1.66	
2.46/1.66	
2.46/1.66	----------------------------------------
2.46/1.66	
2.46/1.66	(0)
2.46/1.66	Obligation:
2.46/1.66	Complexity Int TRS consisting of the following rules:
2.46/1.66	eval_nd_loop_start(v_0, v_x.0) -> Com_1(eval_nd_loop_bb0_in(v_0, v_x.0)) :|: TRUE
2.46/1.66	eval_nd_loop_bb0_in(v_0, v_x.0) -> Com_1(eval_nd_loop_bb1_in(v_0, 0)) :|: TRUE
2.46/1.66	eval_nd_loop_bb1_in(v_0, v_x.0) -> Com_1(eval_nd_loop_0(v_0, v_x.0)) :|: TRUE
2.46/1.66	eval_nd_loop_0(v_0, v_x.0) -> Com_2(eval_nondet_start(v_0, v_x.0), eval_nd_loop_1(nondef.0, v_x.0)) :|: TRUE
2.46/1.66	eval_nd_loop_1(v_0, v_x.0) -> Com_1(eval_nd_loop_bb1_in(v_0, v_0)) :|: v_0 - v_x.0 <= 2 && v_0 - v_x.0 >= 1 && v_0 < 10
2.46/1.66	eval_nd_loop_1(v_0, v_x.0) -> Com_1(eval_nd_loop_bb2_in(v_0, v_x.0)) :|: v_0 - v_x.0 > 2
2.46/1.66	eval_nd_loop_1(v_0, v_x.0) -> Com_1(eval_nd_loop_bb2_in(v_0, v_x.0)) :|: v_0 - v_x.0 < 1
2.46/1.66	eval_nd_loop_1(v_0, v_x.0) -> Com_1(eval_nd_loop_bb2_in(v_0, v_x.0)) :|: v_0 >= 10
2.46/1.66	eval_nd_loop_bb2_in(v_0, v_x.0) -> Com_1(eval_nd_loop_stop(v_0, v_x.0)) :|: TRUE
2.46/1.66	
2.46/1.66	The start-symbols are:[eval_nd_loop_start_2]
2.46/1.66	
2.46/1.66	
2.46/1.66	----------------------------------------
2.46/1.66	
2.46/1.66	(1) Koat Proof (FINISHED)
2.46/1.66	YES(?, 108)
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	Initial complexity problem:
2.46/1.66	
2.46/1.66	1:	T:
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopstart(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.46/1.66	
2.46/1.66	2:	T:
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopstart(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	A polynomial rank function with
2.46/1.66	
2.46/1.66		Pol(evalndloopstart) = 2
2.46/1.66	
2.46/1.66		Pol(evalndloopbb0in) = 2
2.46/1.66	
2.46/1.66		Pol(evalndloopbb1in) = 2
2.46/1.66	
2.46/1.66		Pol(evalndloop0) = 2
2.46/1.66	
2.46/1.66		Pol(evalndloop00) = 0
2.46/1.66	
2.46/1.66		Pol(evalnondetstart) = 0
2.46/1.66	
2.46/1.66		Pol(evalndloop01) = 2
2.46/1.66	
2.46/1.66		Pol(evalndloop1) = 2
2.46/1.66	
2.46/1.66		Pol(evalndloopbb2in) = 1
2.46/1.66	
2.46/1.66		Pol(evalndloopstop) = 0
2.46/1.66	
2.46/1.66		Pol(koat_start) = 2
2.46/1.66	
2.46/1.66	orients all transitions weakly and the transitions
2.46/1.66	
2.46/1.66		evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66		evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66		evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66		evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66	strictly and produces the following problem:
2.46/1.66	
2.46/1.66	3:	T:
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopstart(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d))
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.46/1.66	
2.46/1.66	  For symbol evalndloop0: X_1 >= 0
2.46/1.66	
2.46/1.66	  For symbol evalndloop00: X_1 >= 0
2.46/1.66	
2.46/1.66	  For symbol evalndloop01: X_1 >= 0
2.46/1.66	
2.46/1.66	  For symbol evalndloop1: X_2 - X_3 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 >= 0
2.46/1.66	
2.46/1.66	  For symbol evalndloopbb1in: X_1 >= 0
2.46/1.66	
2.46/1.66	  For symbol evalndloopbb2in: X_2 - X_3 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 >= 0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	This yielded the following problem:
2.46/1.66	
2.46/1.66	4:	T:
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopstart(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	By chaining the transition koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
2.46/1.66	
2.46/1.66		koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66	We thus obtain the following problem:
2.46/1.66	
2.46/1.66	5:	T:
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopstart(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	Testing for reachability in the complexity graph removes the following transition from problem 5:
2.46/1.66	
2.46/1.66		evalndloopstart(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2))
2.46/1.66	
2.46/1.66	We thus obtain the following problem:
2.46/1.66	
2.46/1.66	6:	T:
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	By chaining the transition evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ] with all transitions in problem 6, the following new transition is obtained:
2.46/1.66	
2.46/1.66		evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_1, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.66	
2.46/1.66	We thus obtain the following problem:
2.46/1.66	
2.46/1.66	7:	T:
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 2)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_1, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.46/1.66	
2.46/1.66	8:	T:
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 2)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_1, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	By chaining the transition evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_1, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
2.46/1.66	
2.46/1.66		evalndloop1(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_1, ar_1, d), evalndloop01(ar_1, ar_1, d)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.66	
2.46/1.66	We thus obtain the following problem:
2.46/1.66	
2.46/1.66	9:	T:
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 3)    evalndloop1(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_1, ar_1, d), evalndloop01(ar_1, ar_1, d)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	Repeatedly propagating knowledge in problem 9 produces the following problem:
2.46/1.66	
2.46/1.66	10:	T:
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 3)    evalndloop1(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_1, ar_1, d), evalndloop01(ar_1, ar_1, d)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.66	
2.46/1.66			(Comp: 2, Cost: 1)    evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: ?, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.66	
2.46/1.66			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.66	
2.46/1.66		start location:	koat_start
2.46/1.66	
2.46/1.66		leaf cost:	0
2.46/1.66	
2.46/1.66	
2.46/1.66	
2.46/1.66	A polynomial rank function with
2.46/1.66	
2.46/1.66		Pol(evalndloop1) = -2*V_1 + 18
2.46/1.66	
2.46/1.66		Pol(evalndloop00) = 1
2.46/1.66	
2.46/1.66		Pol(evalndloop01) = -2*V_1 + 18
2.46/1.66	
2.46/1.66		Pol(evalndloopbb2in) = -2*V_1
2.46/1.66	
2.46/1.66		Pol(evalndloopstop) = -2*V_1
2.46/1.66	
2.46/1.66		Pol(evalnondetstart) = 0
2.46/1.66	
2.46/1.66		Pol(evalndloop0) = 19
2.46/1.66	
2.46/1.66		Pol(evalndloopbb1in) = 19
2.46/1.66	
2.46/1.66		Pol(evalndloopbb0in) = 19
2.46/1.66	
2.46/1.66		Pol(koat_start) = 19
2.46/1.66	
2.46/1.66	orients all transitions weakly and the transitions
2.46/1.67	
2.46/1.67		evalndloop1(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_1, ar_1, d), evalndloop01(ar_1, ar_1, d)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.67	
2.46/1.67		evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67	strictly and produces the following problem:
2.46/1.67	
2.46/1.67	11:	T:
2.46/1.67	
2.46/1.67			(Comp: 19, Cost: 3)    evalndloop1(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_1, ar_1, d), evalndloop01(ar_1, ar_1, d)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 2, Cost: 1)     evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 2, Cost: 1)     evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.67	
2.46/1.67			(Comp: 2, Cost: 1)     evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.67	
2.46/1.67			(Comp: 2, Cost: 1)     evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.67	
2.46/1.67			(Comp: 19, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: ?, Cost: 1)     evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 1, Cost: 1)     evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 1, Cost: 1)     evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 1, Cost: 1)     evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.67	
2.46/1.67			(Comp: 1, Cost: 1)     koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.67	
2.46/1.67		start location:	koat_start
2.46/1.67	
2.46/1.67		leaf cost:	0
2.46/1.67	
2.46/1.67	
2.46/1.67	
2.46/1.67	Repeatedly propagating knowledge in problem 11 produces the following problem:
2.46/1.67	
2.46/1.67	12:	T:
2.46/1.67	
2.46/1.67			(Comp: 19, Cost: 3)    evalndloop1(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_1, ar_1, d), evalndloop01(ar_1, ar_1, d)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 /\ ar_1 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 2, Cost: 1)     evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 2, Cost: 1)     evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
2.46/1.67	
2.46/1.67			(Comp: 2, Cost: 1)     evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
2.46/1.67	
2.46/1.67			(Comp: 2, Cost: 1)     evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 10 ]
2.46/1.67	
2.46/1.67			(Comp: 19, Cost: 1)    evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 20, Cost: 1)    evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 1, Cost: 1)     evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 1, Cost: 1)     evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
2.46/1.67	
2.46/1.67			(Comp: 1, Cost: 1)     evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2))
2.46/1.67	
2.46/1.67			(Comp: 1, Cost: 1)     koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.46/1.67	
2.46/1.67		start location:	koat_start
2.46/1.67	
2.46/1.67		leaf cost:	0
2.46/1.67	
2.46/1.67	
2.46/1.67	
2.46/1.67	Complexity upper bound 108
2.46/1.67	
2.46/1.67	
2.46/1.67	
2.46/1.67	Time: 0.390 sec (SMT: 0.317 sec)
2.46/1.67	
2.46/1.67	
2.46/1.67	----------------------------------------
2.46/1.67	
2.46/1.67	(2)
2.46/1.67	BOUNDS(1, 1)
2.53/1.75	EOF