3.48/2.15	WORST_CASE(Omega(n^1), O(n^1))
3.48/2.16	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.48/2.16	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.48/2.16	
3.48/2.16	
3.48/2.16	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
3.48/2.16	
3.48/2.16	(0) CpxIntTrs
3.48/2.16	(1) Koat Proof [FINISHED, 11 ms]
3.48/2.16	(2) BOUNDS(1, n^1)
3.48/2.16	(3) Loat Proof [FINISHED, 437 ms]
3.48/2.16	(4) BOUNDS(n^1, INF)
3.48/2.16	
3.48/2.16	
3.48/2.16	----------------------------------------
3.48/2.16	
3.48/2.16	(0)
3.48/2.16	Obligation:
3.48/2.16	Complexity Int TRS consisting of the following rules:
3.48/2.16	eval_start_start(v_n, v_x_0) -> Com_1(eval_start_bb0_in(v_n, v_x_0)) :|: TRUE
3.48/2.16	eval_start_bb0_in(v_n, v_x_0) -> Com_1(eval_start_0(v_n, v_x_0)) :|: TRUE
3.48/2.16	eval_start_0(v_n, v_x_0) -> Com_1(eval_start_1(v_n, v_x_0)) :|: TRUE
3.48/2.16	eval_start_1(v_n, v_x_0) -> Com_1(eval_start_2(v_n, v_x_0)) :|: TRUE
3.48/2.16	eval_start_2(v_n, v_x_0) -> Com_1(eval_start_3(v_n, v_x_0)) :|: TRUE
3.48/2.16	eval_start_3(v_n, v_x_0) -> Com_1(eval_start_4(v_n, v_x_0)) :|: TRUE
3.48/2.16	eval_start_4(v_n, v_x_0) -> Com_1(eval_start_bb1_in(v_n, 0)) :|: TRUE
3.48/2.16	eval_start_bb1_in(v_n, v_x_0) -> Com_1(eval_start_bb2_in(v_n, v_x_0)) :|: v_x_0 < v_n
3.48/2.16	eval_start_bb1_in(v_n, v_x_0) -> Com_1(eval_start_bb3_in(v_n, v_x_0)) :|: v_x_0 >= v_n
3.48/2.16	eval_start_bb2_in(v_n, v_x_0) -> Com_1(eval_start_5(v_n, v_x_0)) :|: TRUE
3.48/2.16	eval_start_5(v_n, v_x_0) -> Com_1(eval_start_6(v_n, v_x_0)) :|: TRUE
3.48/2.16	eval_start_6(v_n, v_x_0) -> Com_1(eval_start_bb1_in(v_n, v_x_0 + 1)) :|: TRUE
3.48/2.16	eval_start_bb3_in(v_n, v_x_0) -> Com_1(eval_start_stop(v_n, v_x_0)) :|: TRUE
3.48/2.16	
3.48/2.16	The start-symbols are:[eval_start_start_2]
3.48/2.16	
3.48/2.16	
3.48/2.16	----------------------------------------
3.48/2.16	
3.48/2.16	(1) Koat Proof (FINISHED)
3.48/2.16	YES(?, 4*ar_1 + 15)
3.48/2.16	
3.48/2.16	
3.48/2.16	
3.48/2.16	Initial complexity problem:
3.48/2.16	
3.48/2.16	1:	T:
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartstart(ar_0, ar_1) -> Com_1(evalstartbb0in(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb0in(ar_0, ar_1) -> Com_1(evalstart0(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart0(ar_0, ar_1) -> Com_1(evalstart1(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart1(ar_0, ar_1) -> Com_1(evalstart2(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart2(ar_0, ar_1) -> Com_1(evalstart3(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart3(ar_0, ar_1) -> Com_1(evalstart4(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart4(ar_0, ar_1) -> Com_1(evalstartbb1in(0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1) -> Com_1(evalstart5(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart5(ar_0, ar_1) -> Com_1(evalstart6(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart6(ar_0, ar_1) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1) -> Com_1(evalstartstop(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalstartstart(ar_0, ar_1)) [ 0 <= 0 ]
3.48/2.16	
3.48/2.16		start location:	koat_start
3.48/2.16	
3.48/2.16		leaf cost:	0
3.48/2.16	
3.48/2.16	
3.48/2.16	
3.48/2.16	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.48/2.16	
3.48/2.16	2:	T:
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1) -> Com_1(evalstartbb0in(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1) -> Com_1(evalstart0(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1) -> Com_1(evalstart1(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1) -> Com_1(evalstart2(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1) -> Com_1(evalstart3(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1) -> Com_1(evalstart4(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1) -> Com_1(evalstartbb1in(0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1) -> Com_1(evalstart5(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart5(ar_0, ar_1) -> Com_1(evalstart6(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart6(ar_0, ar_1) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1) -> Com_1(evalstartstop(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalstartstart(ar_0, ar_1)) [ 0 <= 0 ]
3.48/2.16	
3.48/2.16		start location:	koat_start
3.48/2.16	
3.48/2.16		leaf cost:	0
3.48/2.16	
3.48/2.16	
3.48/2.16	
3.48/2.16	A polynomial rank function with
3.48/2.16	
3.48/2.16		Pol(evalstartstart) = 2
3.48/2.16	
3.48/2.16		Pol(evalstartbb0in) = 2
3.48/2.16	
3.48/2.16		Pol(evalstart0) = 2
3.48/2.16	
3.48/2.16		Pol(evalstart1) = 2
3.48/2.16	
3.48/2.16		Pol(evalstart2) = 2
3.48/2.16	
3.48/2.16		Pol(evalstart3) = 2
3.48/2.16	
3.48/2.16		Pol(evalstart4) = 2
3.48/2.16	
3.48/2.16		Pol(evalstartbb1in) = 2
3.48/2.16	
3.48/2.16		Pol(evalstartbb2in) = 2
3.48/2.16	
3.48/2.16		Pol(evalstartbb3in) = 1
3.48/2.16	
3.48/2.16		Pol(evalstart5) = 2
3.48/2.16	
3.48/2.16		Pol(evalstart6) = 2
3.48/2.16	
3.48/2.16		Pol(evalstartstop) = 0
3.48/2.16	
3.48/2.16		Pol(koat_start) = 2
3.48/2.16	
3.48/2.16	orients all transitions weakly and the transitions
3.48/2.16	
3.48/2.16		evalstartbb3in(ar_0, ar_1) -> Com_1(evalstartstop(ar_0, ar_1))
3.48/2.16	
3.48/2.16		evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.48/2.16	
3.48/2.16	strictly and produces the following problem:
3.48/2.16	
3.48/2.16	3:	T:
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1) -> Com_1(evalstartbb0in(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1) -> Com_1(evalstart0(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1) -> Com_1(evalstart1(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1) -> Com_1(evalstart2(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1) -> Com_1(evalstart3(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1) -> Com_1(evalstart4(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1) -> Com_1(evalstartbb1in(0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.48/2.16	
3.48/2.16			(Comp: 2, Cost: 1)    evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1) -> Com_1(evalstart5(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart5(ar_0, ar_1) -> Com_1(evalstart6(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: ?, Cost: 1)    evalstart6(ar_0, ar_1) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 2, Cost: 1)    evalstartbb3in(ar_0, ar_1) -> Com_1(evalstartstop(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalstartstart(ar_0, ar_1)) [ 0 <= 0 ]
3.48/2.16	
3.48/2.16		start location:	koat_start
3.48/2.16	
3.48/2.16		leaf cost:	0
3.48/2.16	
3.48/2.16	
3.48/2.16	
3.48/2.16	A polynomial rank function with
3.48/2.16	
3.48/2.16		Pol(evalstartstart) = V_2 + 1
3.48/2.16	
3.48/2.16		Pol(evalstartbb0in) = V_2 + 1
3.48/2.16	
3.48/2.16		Pol(evalstart0) = V_2 + 1
3.48/2.16	
3.48/2.16		Pol(evalstart1) = V_2 + 1
3.48/2.16	
3.48/2.16		Pol(evalstart2) = V_2 + 1
3.48/2.16	
3.48/2.16		Pol(evalstart3) = V_2 + 1
3.48/2.16	
3.48/2.16		Pol(evalstart4) = V_2 + 1
3.48/2.16	
3.48/2.16		Pol(evalstartbb1in) = -V_1 + V_2 + 1
3.48/2.16	
3.48/2.16		Pol(evalstartbb2in) = -V_1 + V_2
3.48/2.16	
3.48/2.16		Pol(evalstartbb3in) = -V_1 + V_2
3.48/2.16	
3.48/2.16		Pol(evalstart5) = -V_1 + V_2
3.48/2.16	
3.48/2.16		Pol(evalstart6) = -V_1 + V_2
3.48/2.16	
3.48/2.16		Pol(evalstartstop) = -V_1 + V_2
3.48/2.16	
3.48/2.16		Pol(koat_start) = V_2 + 1
3.48/2.16	
3.48/2.16	orients all transitions weakly and the transition
3.48/2.16	
3.48/2.16		evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.48/2.16	
3.48/2.16	strictly and produces the following problem:
3.48/2.16	
3.48/2.16	4:	T:
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)           evalstartstart(ar_0, ar_1) -> Com_1(evalstartbb0in(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)           evalstartbb0in(ar_0, ar_1) -> Com_1(evalstart0(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)           evalstart0(ar_0, ar_1) -> Com_1(evalstart1(ar_0, ar_1))
3.48/2.16	
3.48/2.16			(Comp: 1, Cost: 1)           evalstart1(ar_0, ar_1) -> Com_1(evalstart2(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstart2(ar_0, ar_1) -> Com_1(evalstart3(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstart3(ar_0, ar_1) -> Com_1(evalstart4(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstart4(ar_0, ar_1) -> Com_1(evalstartbb1in(0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: ar_1 + 1, Cost: 1)    evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.48/2.17	
3.48/2.17			(Comp: 2, Cost: 1)           evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.48/2.17	
3.48/2.17			(Comp: ?, Cost: 1)           evalstartbb2in(ar_0, ar_1) -> Com_1(evalstart5(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: ?, Cost: 1)           evalstart5(ar_0, ar_1) -> Com_1(evalstart6(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: ?, Cost: 1)           evalstart6(ar_0, ar_1) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 2, Cost: 1)           evalstartbb3in(ar_0, ar_1) -> Com_1(evalstartstop(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1) -> Com_1(evalstartstart(ar_0, ar_1)) [ 0 <= 0 ]
3.48/2.17	
3.48/2.17		start location:	koat_start
3.48/2.17	
3.48/2.17		leaf cost:	0
3.48/2.17	
3.48/2.17	
3.48/2.17	
3.48/2.17	Repeatedly propagating knowledge in problem 4 produces the following problem:
3.48/2.17	
3.48/2.17	5:	T:
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstartstart(ar_0, ar_1) -> Com_1(evalstartbb0in(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstartbb0in(ar_0, ar_1) -> Com_1(evalstart0(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstart0(ar_0, ar_1) -> Com_1(evalstart1(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstart1(ar_0, ar_1) -> Com_1(evalstart2(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstart2(ar_0, ar_1) -> Com_1(evalstart3(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstart3(ar_0, ar_1) -> Com_1(evalstart4(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 1)           evalstart4(ar_0, ar_1) -> Com_1(evalstartbb1in(0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: ar_1 + 1, Cost: 1)    evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.48/2.17	
3.48/2.17			(Comp: 2, Cost: 1)           evalstartbb1in(ar_0, ar_1) -> Com_1(evalstartbb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.48/2.17	
3.48/2.17			(Comp: ar_1 + 1, Cost: 1)    evalstartbb2in(ar_0, ar_1) -> Com_1(evalstart5(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: ar_1 + 1, Cost: 1)    evalstart5(ar_0, ar_1) -> Com_1(evalstart6(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: ar_1 + 1, Cost: 1)    evalstart6(ar_0, ar_1) -> Com_1(evalstartbb1in(ar_0 + 1, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 2, Cost: 1)           evalstartbb3in(ar_0, ar_1) -> Com_1(evalstartstop(ar_0, ar_1))
3.48/2.17	
3.48/2.17			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1) -> Com_1(evalstartstart(ar_0, ar_1)) [ 0 <= 0 ]
3.48/2.17	
3.48/2.17		start location:	koat_start
3.48/2.17	
3.48/2.17		leaf cost:	0
3.48/2.17	
3.48/2.17	
3.48/2.17	
3.48/2.17	Complexity upper bound 4*ar_1 + 15
3.48/2.17	
3.48/2.17	
3.48/2.17	
3.48/2.17	Time: 0.066 sec (SMT: 0.059 sec)
3.48/2.17	
3.48/2.17	
3.48/2.17	----------------------------------------
3.48/2.17	
3.48/2.17	(2)
3.48/2.17	BOUNDS(1, n^1)
3.48/2.17	
3.48/2.17	----------------------------------------
3.48/2.17	
3.48/2.17	(3) Loat Proof (FINISHED)
3.48/2.17	
3.48/2.17	
3.48/2.17	### Pre-processing the ITS problem ###
3.48/2.17	
3.48/2.17	
3.48/2.17	
3.48/2.17	Initial linear ITS problem
3.48/2.17	
3.48/2.17	   Start location: evalstartstart
3.48/2.17	
3.48/2.17	      0: evalstartstart -> evalstartbb0in : [], cost: 1
3.48/2.17	
3.48/2.17	      1: evalstartbb0in -> evalstart0 : [], cost: 1
3.48/2.17	
3.48/2.17	      2: evalstart0 -> evalstart1 : [], cost: 1
3.48/2.17	
3.48/2.17	      3: evalstart1 -> evalstart2 : [], cost: 1
3.48/2.17	
3.48/2.17	      4: evalstart2 -> evalstart3 : [], cost: 1
4.44/2.17	
4.44/2.17	      5: evalstart3 -> evalstart4 : [], cost: 1
4.44/2.17	
4.44/2.17	      6: evalstart4 -> evalstartbb1in : A'=0, [], cost: 1
4.44/2.17	
4.44/2.17	      7: evalstartbb1in -> evalstartbb2in : [ B>=1+A ], cost: 1
4.44/2.17	
4.44/2.17	      8: evalstartbb1in -> evalstartbb3in : [ A>=B ], cost: 1
4.44/2.17	
4.44/2.17	      9: evalstartbb2in -> evalstart5 : [], cost: 1
4.44/2.17	
4.44/2.17	     10: evalstart5 -> evalstart6 : [], cost: 1
4.44/2.17	
4.44/2.17	     11: evalstart6 -> evalstartbb1in : A'=1+A, [], cost: 1
4.44/2.17	
4.44/2.17	     12: evalstartbb3in -> evalstartstop : [], cost: 1
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Removed unreachable and leaf rules:
4.44/2.17	
4.44/2.17	   Start location: evalstartstart
4.44/2.17	
4.44/2.17	      0: evalstartstart -> evalstartbb0in : [], cost: 1
4.44/2.17	
4.44/2.17	      1: evalstartbb0in -> evalstart0 : [], cost: 1
4.44/2.17	
4.44/2.17	      2: evalstart0 -> evalstart1 : [], cost: 1
4.44/2.17	
4.44/2.17	      3: evalstart1 -> evalstart2 : [], cost: 1
4.44/2.17	
4.44/2.17	      4: evalstart2 -> evalstart3 : [], cost: 1
4.44/2.17	
4.44/2.17	      5: evalstart3 -> evalstart4 : [], cost: 1
4.44/2.17	
4.44/2.17	      6: evalstart4 -> evalstartbb1in : A'=0, [], cost: 1
4.44/2.17	
4.44/2.17	      7: evalstartbb1in -> evalstartbb2in : [ B>=1+A ], cost: 1
4.44/2.17	
4.44/2.17	      9: evalstartbb2in -> evalstart5 : [], cost: 1
4.44/2.17	
4.44/2.17	     10: evalstart5 -> evalstart6 : [], cost: 1
4.44/2.17	
4.44/2.17	     11: evalstart6 -> evalstartbb1in : A'=1+A, [], cost: 1
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	### Simplification by acceleration and chaining ###
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Eliminated locations (on linear paths):
4.44/2.17	
4.44/2.17	   Start location: evalstartstart
4.44/2.17	
4.44/2.17	     18: evalstartstart -> evalstartbb1in : A'=0, [], cost: 7
4.44/2.17	
4.44/2.17	     21: evalstartbb1in -> evalstartbb1in : A'=1+A, [ B>=1+A ], cost: 4
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Accelerating simple loops of location 7.
4.44/2.17	
4.44/2.17	   Accelerating the following rules:
4.44/2.17	
4.44/2.17	     21: evalstartbb1in -> evalstartbb1in : A'=1+A, [ B>=1+A ], cost: 4
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	   Accelerated rule 21 with metering function -A+B, yielding the new rule 22.
4.44/2.17	
4.44/2.17	   Removing the simple loops: 21.
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Accelerated all simple loops using metering functions (where possible):
4.44/2.17	
4.44/2.17	   Start location: evalstartstart
4.44/2.17	
4.44/2.17	     18: evalstartstart -> evalstartbb1in : A'=0, [], cost: 7
4.44/2.17	
4.44/2.17	     22: evalstartbb1in -> evalstartbb1in : A'=B, [ B>=1+A ], cost: -4*A+4*B
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Chained accelerated rules (with incoming rules):
4.44/2.17	
4.44/2.17	   Start location: evalstartstart
4.44/2.17	
4.44/2.17	     18: evalstartstart -> evalstartbb1in : A'=0, [], cost: 7
4.44/2.17	
4.44/2.17	     23: evalstartstart -> evalstartbb1in : A'=B, [ B>=1 ], cost: 7+4*B
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Removed unreachable locations (and leaf rules with constant cost):
4.44/2.17	
4.44/2.17	   Start location: evalstartstart
4.44/2.17	
4.44/2.17	     23: evalstartstart -> evalstartbb1in : A'=B, [ B>=1 ], cost: 7+4*B
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	### Computing asymptotic complexity ###
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Fully simplified ITS problem
4.44/2.17	
4.44/2.17	   Start location: evalstartstart
4.44/2.17	
4.44/2.17	     23: evalstartstart -> evalstartbb1in : A'=B, [ B>=1 ], cost: 7+4*B
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Computing asymptotic complexity for rule 23
4.44/2.17	
4.44/2.17	   Solved the limit problem by the following transformations:
4.44/2.17	
4.44/2.17	      Created initial limit problem:
4.44/2.17	
4.44/2.17	      7+4*B (+), B (+/+!) [not solved]
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	      removing all constraints (solved by SMT)
4.44/2.17	
4.44/2.17	      resulting limit problem: [solved]
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	      applying transformation rule (C) using substitution {B==n}
4.44/2.17	
4.44/2.17	      resulting limit problem:
4.44/2.17	
4.44/2.17	      [solved]
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	   Solution:
4.44/2.17	
4.44/2.17	      B / n
4.44/2.17	
4.44/2.17	   Resulting cost 7+4*n has complexity: Poly(n^1)
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Found new complexity Poly(n^1).
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	Obtained the following overall complexity (w.r.t. the length of the input n):
4.44/2.17	
4.44/2.17	   Complexity:  Poly(n^1)
4.44/2.17	
4.44/2.17	   Cpx degree:  1
4.44/2.17	
4.44/2.17	   Solved cost: 7+4*n
4.44/2.17	
4.44/2.17	   Rule cost:   7+4*B
4.44/2.17	
4.44/2.17	   Rule guard:  [ B>=1 ]
4.44/2.17	
4.44/2.17	
4.44/2.17	
4.44/2.17	WORST_CASE(Omega(n^1),?)
4.44/2.17	
4.44/2.17	
4.44/2.17	----------------------------------------
4.44/2.17	
4.44/2.17	(4)
4.44/2.17	BOUNDS(n^1, INF)
4.44/2.19	EOF