5.27/2.49	WORST_CASE(Omega(n^1), O(n^1))
5.27/2.50	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
5.27/2.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.27/2.50	
5.27/2.50	
5.27/2.50	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.27/2.50	
5.27/2.50	(0) CpxIntTrs
5.27/2.50	(1) Koat Proof [FINISHED, 345 ms]
5.27/2.50	(2) BOUNDS(1, n^1)
5.27/2.50	(3) Loat Proof [FINISHED, 823 ms]
5.27/2.50	(4) BOUNDS(n^1, INF)
5.27/2.50	
5.27/2.50	
5.27/2.50	----------------------------------------
5.27/2.50	
5.27/2.50	(0)
5.27/2.50	Obligation:
5.27/2.50	Complexity Int TRS consisting of the following rules:
5.27/2.50	eval_start_start(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb0_in(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_bb0_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_0(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_0(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_1(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_1(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_2(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_2(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_3(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_3(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_4(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_4(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb1_in(v_m, v_n, v_n, 0)) :|: v_m > 0
5.27/2.50	eval_start_4(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb5_in(v_m, v_n, v_va_0, v_vb_0)) :|: v_m <= 0
5.27/2.50	eval_start_bb1_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb2_in(v_m, v_n, v_va_0, v_vb_0)) :|: v_va_0 > 0
5.27/2.50	eval_start_bb1_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb4_in(v_m, v_n, v_va_0, v_vb_0)) :|: v_va_0 <= 0
5.27/2.50	eval_start_bb2_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb3_in(v_m, v_n, v_va_0, v_vb_0)) :|: v_vb_0 < v_m
5.27/2.50	eval_start_bb2_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb1_in(v_m, v_n, v_va_0, 0)) :|: v_vb_0 >= v_m
5.27/2.50	eval_start_bb3_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_bb1_in(v_m, v_n, v_va_0 - 1, v_vb_0 + 1)) :|: TRUE
5.27/2.50	eval_start_bb4_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_stop(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_bb5_in(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_8(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_8(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_9(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	eval_start_9(v_m, v_n, v_va_0, v_vb_0) -> Com_1(eval_start_stop(v_m, v_n, v_va_0, v_vb_0)) :|: TRUE
5.27/2.50	
5.27/2.50	The start-symbols are:[eval_start_start_4]
5.27/2.50	
5.27/2.50	
5.27/2.50	----------------------------------------
5.27/2.50	
5.27/2.50	(1) Koat Proof (FINISHED)
5.27/2.50	YES(?, 20*ar_2 + 19)
5.27/2.50	
5.27/2.50	
5.27/2.50	
5.27/2.50	Initial complexity problem:
5.27/2.50	
5.27/2.50	1:	T:
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.27/2.50	
5.27/2.50		start location:	koat_start
5.27/2.50	
5.27/2.50		leaf cost:	0
5.27/2.50	
5.27/2.50	
5.27/2.50	
5.27/2.50	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.27/2.50	
5.27/2.50	2:	T:
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1))
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.27/2.50	
5.27/2.50		start location:	koat_start
5.27/2.50	
5.27/2.50		leaf cost:	0
5.27/2.50	
5.27/2.50	
5.27/2.50	
5.27/2.50	A polynomial rank function with
5.27/2.50	
5.27/2.50		Pol(evalstartstart) = 2
5.27/2.50	
5.27/2.50		Pol(evalstartbb0in) = 2
5.27/2.50	
5.27/2.50		Pol(evalstart0) = 2
5.27/2.50	
5.27/2.50		Pol(evalstart1) = 2
5.27/2.50	
5.27/2.50		Pol(evalstart2) = 2
5.27/2.50	
5.27/2.50		Pol(evalstart3) = 2
5.27/2.50	
5.27/2.50		Pol(evalstart4) = 2
5.27/2.50	
5.27/2.50		Pol(evalstartbb1in) = 2
5.27/2.50	
5.27/2.50		Pol(evalstartbb5in) = 0
5.27/2.50	
5.27/2.50		Pol(evalstartbb2in) = 2
5.27/2.50	
5.27/2.50		Pol(evalstartbb4in) = 1
5.27/2.50	
5.27/2.50		Pol(evalstartbb3in) = 2
5.27/2.50	
5.27/2.50		Pol(evalstartstop) = 0
5.27/2.50	
5.27/2.50		Pol(evalstart8) = 0
5.27/2.50	
5.27/2.50		Pol(evalstart9) = 0
5.27/2.50	
5.27/2.50		Pol(koat_start) = 2
5.27/2.50	
5.27/2.50	orients all transitions weakly and the transitions
5.27/2.50	
5.27/2.50		evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50		evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.27/2.50	
5.27/2.50	strictly and produces the following problem:
5.27/2.50	
5.27/2.50	3:	T:
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 1 ]
5.27/2.50	
5.27/2.50			(Comp: 2, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1))
5.27/2.50	
5.27/2.50			(Comp: 2, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.27/2.50	
5.27/2.50		start location:	koat_start
5.27/2.50	
5.27/2.50		leaf cost:	0
5.27/2.50	
5.27/2.50	
5.27/2.50	
5.27/2.50	Applied AI with 'oct' on problem 3 to obtain the following invariants:
5.27/2.50	
5.27/2.50	  For symbol evalstart8: -X_1 >= 0
5.27/2.50	
5.27/2.50	  For symbol evalstart9: -X_1 >= 0
5.27/2.50	
5.27/2.50	  For symbol evalstartbb1in: X_4 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 - 1 >= 0
5.27/2.50	
5.27/2.50	  For symbol evalstartbb2in: X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
5.27/2.50	
5.27/2.50	  For symbol evalstartbb3in: X_1 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
5.27/2.50	
5.27/2.50	  For symbol evalstartbb4in: X_4 >= 0 /\ -X_2 + X_4 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_2 + X_3 >= 0 /\ -X_2 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.27/2.50	
5.27/2.50	  For symbol evalstartbb5in: -X_1 >= 0
5.27/2.50	
5.27/2.50	
5.27/2.50	
5.27/2.50	
5.27/2.50	
5.27/2.50	This yielded the following problem:
5.27/2.50	
5.27/2.50	4:	T:
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]
5.27/2.50	
5.27/2.50			(Comp: 2, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ -ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ -ar_1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
5.27/2.50	
5.27/2.50			(Comp: 2, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_1 ]
5.27/2.50	
5.27/2.50			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))
5.27/2.50	
5.27/2.50		start location:	koat_start
5.27/2.50	
5.27/2.50		leaf cost:	0
5.27/2.50	
5.27/2.50	
5.27/2.50	
5.27/2.50	A polynomial rank function with
5.27/2.50	
5.27/2.50		Pol(evalstartbb3in) = 5*V_2 + 2*V_4 - 1
5.27/2.50	
5.27/2.50		Pol(evalstartbb1in) = 5*V_2 + 2*V_4 + 1
5.27/2.50	
5.27/2.50		Pol(evalstartbb2in) = 5*V_2 + 2*V_4
5.27/2.50	
5.27/2.50	and size complexities
5.27/2.50	
5.27/2.50		S("evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]", 0-1) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]", 0-3) = 0
5.27/2.50	
5.27/2.50		S("evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-1) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-3) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-1) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-3) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-1) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_3 + 1 ]", 0-3) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-1) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_0 ]", 0-3) = 0
5.27/2.50	
5.27/2.50		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ -ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ -ar_1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ -ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ -ar_1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ -ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ -ar_1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ -ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ -ar_1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]", 0-3) = ar_3
5.27/2.50	
5.27/2.50		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.27/2.50	
5.27/2.50		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.27/2.50	
5.27/2.50		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.27/2.50	
5.27/2.50		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.27/2.50	
5.27/2.50	orients the transitions
5.27/2.50	
5.27/2.50		evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
5.27/2.50	
5.27/2.50		evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
5.27/2.50	
5.27/2.50		evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
5.27/2.50	
5.27/2.50		evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
5.27/2.50	
5.27/2.50	weakly and the transitions
5.27/2.50	
5.27/2.50		evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
5.27/2.50	
5.27/2.50		evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
5.27/2.50	
5.27/2.50		evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
5.27/2.50	
5.27/2.50		evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
5.27/2.50	
5.27/2.50	strictly and produces the following problem:
5.27/2.50	
5.27/2.50	5:	T:
5.27/2.50	
5.27/2.50			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstart9(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstart8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstartbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 >= 0 ]
5.49/2.50	
5.49/2.50			(Comp: 2, Cost: 1)             evalstartbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ -ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ -ar_1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.49/2.50	
5.49/2.50			(Comp: 5*ar_2 + 1, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1 - 1, ar_2, ar_3 + 1)) [ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
5.49/2.50	
5.49/2.50			(Comp: 5*ar_2 + 1, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_0 ]
5.49/2.50	
5.49/2.50			(Comp: 5*ar_2 + 1, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_3 + 1 ]
5.49/2.50	
5.49/2.50			(Comp: 2, Cost: 1)             evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_1 ]
5.49/2.50	
5.49/2.50			(Comp: 5*ar_2 + 1, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstart4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, 0)) [ ar_0 >= 1 ]
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstart3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3))
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstart2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3))
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstart1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3))
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstart0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3))
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstartbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3))
5.49/2.50	
5.49/2.50			(Comp: 1, Cost: 1)             evalstartstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3))
5.49/2.50	
5.49/2.50		start location:	koat_start
5.49/2.50	
5.49/2.50		leaf cost:	0
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Complexity upper bound 20*ar_2 + 19
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Time: 0.356 sec (SMT: 0.278 sec)
5.49/2.50	
5.49/2.50	
5.49/2.50	----------------------------------------
5.49/2.50	
5.49/2.50	(2)
5.49/2.50	BOUNDS(1, n^1)
5.49/2.50	
5.49/2.50	----------------------------------------
5.49/2.50	
5.49/2.50	(3) Loat Proof (FINISHED)
5.49/2.50	
5.49/2.50	
5.49/2.50	### Pre-processing the ITS problem ###
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Initial linear ITS problem
5.49/2.50	
5.49/2.50	   Start location: evalstartstart
5.49/2.50	
5.49/2.50	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.49/2.50	
5.49/2.50	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.49/2.50	
5.49/2.50	      2: evalstart0 -> evalstart1 : [], cost: 1
5.49/2.50	
5.49/2.50	      3: evalstart1 -> evalstart2 : [], cost: 1
5.49/2.50	
5.49/2.50	      4: evalstart2 -> evalstart3 : [], cost: 1
5.49/2.50	
5.49/2.50	      5: evalstart3 -> evalstart4 : [], cost: 1
5.49/2.50	
5.49/2.50	      6: evalstart4 -> evalstartbb1in : B'=C, D'=0, [ A>=1 ], cost: 1
5.49/2.50	
5.49/2.50	      7: evalstart4 -> evalstartbb5in : [ 0>=A ], cost: 1
5.49/2.50	
5.49/2.50	      8: evalstartbb1in -> evalstartbb2in : [ B>=1 ], cost: 1
5.49/2.50	
5.49/2.50	      9: evalstartbb1in -> evalstartbb4in : [ 0>=B ], cost: 1
5.49/2.50	
5.49/2.50	     10: evalstartbb2in -> evalstartbb3in : [ A>=1+D ], cost: 1
5.49/2.50	
5.49/2.50	     11: evalstartbb2in -> evalstartbb1in : D'=0, [ D>=A ], cost: 1
5.49/2.50	
5.49/2.50	     12: evalstartbb3in -> evalstartbb1in : B'=-1+B, D'=1+D, [], cost: 1
5.49/2.50	
5.49/2.50	     13: evalstartbb4in -> evalstartstop : [], cost: 1
5.49/2.50	
5.49/2.50	     14: evalstartbb5in -> evalstart8 : [], cost: 1
5.49/2.50	
5.49/2.50	     15: evalstart8 -> evalstart9 : [], cost: 1
5.49/2.50	
5.49/2.50	     16: evalstart9 -> evalstartstop : [], cost: 1
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Removed unreachable and leaf rules:
5.49/2.50	
5.49/2.50	   Start location: evalstartstart
5.49/2.50	
5.49/2.50	      0: evalstartstart -> evalstartbb0in : [], cost: 1
5.49/2.50	
5.49/2.50	      1: evalstartbb0in -> evalstart0 : [], cost: 1
5.49/2.50	
5.49/2.50	      2: evalstart0 -> evalstart1 : [], cost: 1
5.49/2.50	
5.49/2.50	      3: evalstart1 -> evalstart2 : [], cost: 1
5.49/2.50	
5.49/2.50	      4: evalstart2 -> evalstart3 : [], cost: 1
5.49/2.50	
5.49/2.50	      5: evalstart3 -> evalstart4 : [], cost: 1
5.49/2.50	
5.49/2.50	      6: evalstart4 -> evalstartbb1in : B'=C, D'=0, [ A>=1 ], cost: 1
5.49/2.50	
5.49/2.50	      8: evalstartbb1in -> evalstartbb2in : [ B>=1 ], cost: 1
5.49/2.50	
5.49/2.50	     10: evalstartbb2in -> evalstartbb3in : [ A>=1+D ], cost: 1
5.49/2.50	
5.49/2.50	     11: evalstartbb2in -> evalstartbb1in : D'=0, [ D>=A ], cost: 1
5.49/2.50	
5.49/2.50	     12: evalstartbb3in -> evalstartbb1in : B'=-1+B, D'=1+D, [], cost: 1
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	### Simplification by acceleration and chaining ###
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Eliminated locations (on linear paths):
5.49/2.50	
5.49/2.50	   Start location: evalstartstart
5.49/2.50	
5.49/2.50	     22: evalstartstart -> evalstartbb1in : B'=C, D'=0, [ A>=1 ], cost: 7
5.49/2.50	
5.49/2.50	      8: evalstartbb1in -> evalstartbb2in : [ B>=1 ], cost: 1
5.49/2.50	
5.49/2.50	     11: evalstartbb2in -> evalstartbb1in : D'=0, [ D>=A ], cost: 1
5.49/2.50	
5.49/2.50	     23: evalstartbb2in -> evalstartbb1in : B'=-1+B, D'=1+D, [ A>=1+D ], cost: 2
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Eliminated locations (on tree-shaped paths):
5.49/2.50	
5.49/2.50	   Start location: evalstartstart
5.49/2.50	
5.49/2.50	     22: evalstartstart -> evalstartbb1in : B'=C, D'=0, [ A>=1 ], cost: 7
5.49/2.50	
5.49/2.50	     24: evalstartbb1in -> evalstartbb1in : D'=0, [ B>=1 && D>=A ], cost: 2
5.49/2.50	
5.49/2.50	     25: evalstartbb1in -> evalstartbb1in : B'=-1+B, D'=1+D, [ B>=1 && A>=1+D ], cost: 3
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Accelerating simple loops of location 7.
5.49/2.50	
5.49/2.50	   Accelerating the following rules:
5.49/2.50	
5.49/2.50	     24: evalstartbb1in -> evalstartbb1in : D'=0, [ B>=1 && D>=A ], cost: 2
5.49/2.50	
5.49/2.50	     25: evalstartbb1in -> evalstartbb1in : B'=-1+B, D'=1+D, [ B>=1 && A>=1+D ], cost: 3
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	   Accelerated rule 24 with NONTERM (after strengthening guard), yielding the new rule 26.
5.49/2.50	
5.49/2.50	   Accelerated rule 25 with backward acceleration, yielding the new rule 27.
5.49/2.50	
5.49/2.50	   Accelerated rule 25 with backward acceleration, yielding the new rule 28.
5.49/2.50	
5.49/2.50	   Removing the simple loops: 25.
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Accelerated all simple loops using metering functions (where possible):
5.49/2.50	
5.49/2.50	   Start location: evalstartstart
5.49/2.50	
5.49/2.50	     22: evalstartstart -> evalstartbb1in : B'=C, D'=0, [ A>=1 ], cost: 7
5.49/2.50	
5.49/2.50	     24: evalstartbb1in -> evalstartbb1in : D'=0, [ B>=1 && D>=A ], cost: 2
5.49/2.50	
5.49/2.50	     26: evalstartbb1in -> [15] : [ B>=1 && D>=A && 0>=A ], cost: INF
5.49/2.50	
5.49/2.50	     27: evalstartbb1in -> evalstartbb1in : B'=0, D'=D+B, [ B>=1 && A>=1+D && A>=D+B ], cost: 3*B
5.49/2.50	
5.49/2.50	     28: evalstartbb1in -> evalstartbb1in : B'=D-A+B, D'=A, [ B>=1 && A>=1+D && 1+D-A+B>=1 ], cost: -3*D+3*A
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Chained accelerated rules (with incoming rules):
5.49/2.50	
5.49/2.50	   Start location: evalstartstart
5.49/2.50	
5.49/2.50	     22: evalstartstart -> evalstartbb1in : B'=C, D'=0, [ A>=1 ], cost: 7
5.49/2.50	
5.49/2.50	     29: evalstartstart -> evalstartbb1in : B'=0, D'=C, [ A>=1 && C>=1 && A>=C ], cost: 7+3*C
5.49/2.50	
5.49/2.50	     30: evalstartstart -> evalstartbb1in : B'=C-A, D'=A, [ A>=1 && C>=1 && 1+C-A>=1 ], cost: 7+3*A
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Removed unreachable locations (and leaf rules with constant cost):
5.49/2.50	
5.49/2.50	   Start location: evalstartstart
5.49/2.50	
5.49/2.50	     29: evalstartstart -> evalstartbb1in : B'=0, D'=C, [ A>=1 && C>=1 && A>=C ], cost: 7+3*C
5.49/2.50	
5.49/2.50	     30: evalstartstart -> evalstartbb1in : B'=C-A, D'=A, [ A>=1 && C>=1 && 1+C-A>=1 ], cost: 7+3*A
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	### Computing asymptotic complexity ###
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Fully simplified ITS problem
5.49/2.50	
5.49/2.50	   Start location: evalstartstart
5.49/2.50	
5.49/2.50	     29: evalstartstart -> evalstartbb1in : B'=0, D'=C, [ A>=1 && C>=1 && A>=C ], cost: 7+3*C
5.49/2.50	
5.49/2.50	     30: evalstartstart -> evalstartbb1in : B'=C-A, D'=A, [ A>=1 && C>=1 && 1+C-A>=1 ], cost: 7+3*A
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Computing asymptotic complexity for rule 29
5.49/2.50	
5.49/2.50	   Simplified the guard:
5.49/2.50	
5.49/2.50	     29: evalstartstart -> evalstartbb1in : B'=0, D'=C, [ C>=1 && A>=C ], cost: 7+3*C
5.49/2.50	
5.49/2.50	   Solved the limit problem by the following transformations:
5.49/2.50	
5.49/2.50	      Created initial limit problem:
5.49/2.50	
5.49/2.50	      C (+/+!), 1-C+A (+/+!), 7+3*C (+) [not solved]
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	      removing all constraints (solved by SMT)
5.49/2.50	
5.49/2.50	      resulting limit problem: [solved]
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	      applying transformation rule (C) using substitution {C==n,A==n}
5.49/2.50	
5.49/2.50	      resulting limit problem:
5.49/2.50	
5.49/2.50	      [solved]
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	   Solution:
5.49/2.50	
5.49/2.50	      C / n
5.49/2.50	
5.49/2.50	      A / n
5.49/2.50	
5.49/2.50	   Resulting cost 7+3*n has complexity: Poly(n^1)
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Found new complexity Poly(n^1).
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	Obtained the following overall complexity (w.r.t. the length of the input n):
5.49/2.50	
5.49/2.50	   Complexity:  Poly(n^1)
5.49/2.50	
5.49/2.50	   Cpx degree:  1
5.49/2.50	
5.49/2.50	   Solved cost: 7+3*n
5.49/2.50	
5.49/2.50	   Rule cost:   7+3*C
5.49/2.50	
5.49/2.50	   Rule guard:  [ C>=1 && A>=C ]
5.49/2.50	
5.49/2.50	
5.49/2.50	
5.49/2.50	WORST_CASE(Omega(n^1),?)
5.49/2.50	
5.49/2.50	
5.49/2.50	----------------------------------------
5.49/2.50	
5.49/2.50	(4)
5.49/2.50	BOUNDS(n^1, INF)
5.49/2.53	EOF