4.90/2.32	WORST_CASE(Omega(n^1), O(n^1))
4.90/2.33	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.90/2.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.90/2.33	
4.90/2.33	
4.90/2.33	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.90/2.33	
4.90/2.33	(0) CpxIntTrs
4.90/2.33	(1) Koat Proof [FINISHED, 119 ms]
4.90/2.33	(2) BOUNDS(1, n^1)
4.90/2.33	(3) Loat Proof [FINISHED, 622 ms]
4.90/2.33	(4) BOUNDS(n^1, INF)
4.90/2.33	
4.90/2.33	
4.90/2.33	----------------------------------------
4.90/2.33	
4.90/2.33	(0)
4.90/2.33	Obligation:
4.90/2.33	Complexity Int TRS consisting of the following rules:
4.90/2.33	eval_start_start(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_bb0_in(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: TRUE
4.90/2.33	eval_start_bb0_in(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_0(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: TRUE
4.90/2.33	eval_start_0(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_1(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: TRUE
4.90/2.33	eval_start_1(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_2(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: TRUE
4.90/2.33	eval_start_2(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_3(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: TRUE
4.90/2.33	eval_start_3(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_4(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: TRUE
4.90/2.33	eval_start_4(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_5(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: TRUE
4.90/2.33	eval_start_5(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_bb1_in(v_n, v__1, 1, v_flag_1, v_n)) :|: TRUE
4.90/2.33	eval_start_bb1_in(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_bb2_in(v__0, v__0, v_flag_0, 0, v_n)) :|: v_flag_0 > 0
4.90/2.33	eval_start_bb1_in(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_bb4_in(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: v_flag_0 <= 0
4.90/2.33	eval_start_bb2_in(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_bb3_in(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: v__1 > 0
4.90/2.33	eval_start_bb2_in(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_bb1_in(v__1, v__1, v_flag_1, v_flag_1, v_n)) :|: v__1 <= 0
4.90/2.33	eval_start_bb3_in(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_bb2_in(v__0, v__1 - 1, v_flag_0, 1, v_n)) :|: TRUE
4.90/2.33	eval_start_bb4_in(v__0, v__1, v_flag_0, v_flag_1, v_n) -> Com_1(eval_start_stop(v__0, v__1, v_flag_0, v_flag_1, v_n)) :|: TRUE
4.90/2.33	
4.90/2.33	The start-symbols are:[eval_start_start_5]
4.90/2.33	
4.90/2.33	
4.90/2.33	----------------------------------------
4.90/2.33	
4.90/2.33	(1) Koat Proof (FINISHED)
4.90/2.33	YES(?, 5*ar_1 + 14)
4.90/2.33	
4.90/2.33	
4.90/2.33	
4.90/2.33	Initial complexity problem:
4.90/2.33	
4.90/2.33	1:	T:
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.90/2.33	
4.90/2.33		start location:	koat_start
4.90/2.33	
4.90/2.33		leaf cost:	0
4.90/2.33	
4.90/2.33	
4.90/2.33	
4.90/2.33	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.90/2.33	
4.90/2.33	2:	T:
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.90/2.33	
4.90/2.33		start location:	koat_start
4.90/2.33	
4.90/2.33		leaf cost:	0
4.90/2.33	
4.90/2.33	
4.90/2.33	
4.90/2.33	A polynomial rank function with
4.90/2.33	
4.90/2.33		Pol(evalstartstart) = 2
4.90/2.33	
4.90/2.33		Pol(evalstartbb0in) = 2
4.90/2.33	
4.90/2.33		Pol(evalstart0) = 2
4.90/2.33	
4.90/2.33		Pol(evalstart1) = 2
4.90/2.33	
4.90/2.33		Pol(evalstart2) = 2
4.90/2.33	
4.90/2.33		Pol(evalstart3) = 2
4.90/2.33	
4.90/2.33		Pol(evalstart4) = 2
4.90/2.33	
4.90/2.33		Pol(evalstart5) = 2
4.90/2.33	
4.90/2.33		Pol(evalstartbb1in) = 2
4.90/2.33	
4.90/2.33		Pol(evalstartbb2in) = 2
4.90/2.33	
4.90/2.33		Pol(evalstartbb4in) = 1
4.90/2.33	
4.90/2.33		Pol(evalstartbb3in) = 2
4.90/2.33	
4.90/2.33		Pol(evalstartstop) = 0
4.90/2.33	
4.90/2.33		Pol(koat_start) = 2
4.90/2.33	
4.90/2.33	orients all transitions weakly and the transitions
4.90/2.33	
4.90/2.33		evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
4.90/2.33	
4.90/2.33	strictly and produces the following problem:
4.90/2.33	
4.90/2.33	3:	T:
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 1)    evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.33	
4.90/2.33			(Comp: 2, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
4.90/2.33	
4.90/2.33			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
4.90/2.33	
4.90/2.33			(Comp: 2, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.33	
4.90/2.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.90/2.33	
4.90/2.33		start location:	koat_start
4.90/2.33	
4.90/2.33		leaf cost:	0
4.90/2.33	
4.90/2.33	
4.90/2.33	
4.90/2.33	A polynomial rank function with
4.90/2.33	
4.90/2.33		Pol(evalstartstart) = V_2
4.90/2.33	
4.90/2.33		Pol(evalstartbb0in) = V_2
4.90/2.33	
4.90/2.33		Pol(evalstart0) = V_2
4.90/2.33	
4.90/2.33		Pol(evalstart1) = V_2
4.90/2.33	
4.90/2.33		Pol(evalstart2) = V_2
4.90/2.33	
4.90/2.33		Pol(evalstart3) = V_2
4.90/2.33	
4.90/2.33		Pol(evalstart4) = V_2
4.90/2.33	
4.90/2.33		Pol(evalstart5) = V_2
4.90/2.33	
4.90/2.33		Pol(evalstartbb1in) = V_1
4.90/2.34	
4.90/2.34		Pol(evalstartbb2in) = V_4
4.90/2.34	
4.90/2.34		Pol(evalstartbb4in) = V_1
4.90/2.34	
4.90/2.34		Pol(evalstartbb3in) = V_4 - 1
4.90/2.34	
4.90/2.34		Pol(evalstartstop) = V_1
4.90/2.34	
4.90/2.34		Pol(koat_start) = V_2
4.90/2.34	
4.90/2.34	orients all transitions weakly and the transition
4.90/2.34	
4.90/2.34		evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
4.90/2.34	
4.90/2.34	strictly and produces the following problem:
4.90/2.34	
4.90/2.34	4:	T:
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: ?, Cost: 1)       evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.34	
4.90/2.34			(Comp: 2, Cost: 1)       evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
4.90/2.34	
4.90/2.34			(Comp: ar_1, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
4.90/2.34	
4.90/2.34			(Comp: ?, Cost: 1)       evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
4.90/2.34	
4.90/2.34			(Comp: ?, Cost: 1)       evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
4.90/2.34	
4.90/2.34			(Comp: 2, Cost: 1)       evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.90/2.34	
4.90/2.34		start location:	koat_start
4.90/2.34	
4.90/2.34		leaf cost:	0
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.90/2.34	
4.90/2.34	5:	T:
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)       evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: ?, Cost: 1)       evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.34	
4.90/2.34			(Comp: 2, Cost: 1)       evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
4.90/2.34	
4.90/2.34			(Comp: ar_1, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
4.90/2.34	
4.90/2.34			(Comp: ?, Cost: 1)       evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
4.90/2.34	
4.90/2.34			(Comp: ar_1, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
4.90/2.34	
4.90/2.34			(Comp: 2, Cost: 1)       evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.90/2.34	
4.90/2.34		start location:	koat_start
4.90/2.34	
4.90/2.34		leaf cost:	0
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	A polynomial rank function with
4.90/2.34	
4.90/2.34		Pol(evalstartbb2in) = V_5
4.90/2.34	
4.90/2.34		Pol(evalstartbb1in) = V_3
4.90/2.34	
4.90/2.34	and size complexities
4.90/2.34	
4.90/2.34		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
4.90/2.34	
4.90/2.34		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
4.90/2.34	
4.90/2.34		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
4.90/2.34	
4.90/2.34		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-0) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-2) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-3) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-4) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-0) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-2) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-3) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-4) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-0) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-2) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-3) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-4) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-0) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-2) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-3) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-4) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-0) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-2) = 1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-3) = 2*ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-4) = 0
4.90/2.34	
4.90/2.34		S("evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-0) = ar_1
4.90/2.34	
4.90/2.34		S("evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-2) = 1
4.90/2.34	
4.90/2.34		S("evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-4) = ar_4
4.90/2.34	
4.90/2.34		S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.90/2.34	
4.90/2.34		S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.90/2.34	
4.90/2.34		S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.90/2.34	
4.90/2.34		S("evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.90/2.34	
4.90/2.34		S("evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.90/2.34	
4.90/2.34		S("evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.90/2.34	
4.90/2.34		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.90/2.34	
4.90/2.34		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.90/2.34	
4.90/2.34		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.90/2.34	
4.90/2.34		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.90/2.34	
4.90/2.34		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.90/2.34	
4.90/2.34		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.90/2.34	
4.90/2.34		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.90/2.34	
4.90/2.34		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.90/2.34	
4.90/2.34		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.90/2.34	
4.90/2.34		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.90/2.34	
4.90/2.34		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.90/2.34	
4.90/2.34		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.90/2.34	
4.90/2.34		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.90/2.34	
4.90/2.34		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.90/2.34	
4.90/2.34		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.90/2.34	
4.90/2.34		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.90/2.34	
4.90/2.34		S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.90/2.34	
4.90/2.34	orients the transitions
4.90/2.34	
4.90/2.34		evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
4.90/2.34	
4.90/2.34		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.34	
4.90/2.34	weakly and the transition
4.90/2.34	
4.90/2.34		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.34	
4.90/2.34	strictly and produces the following problem:
4.90/2.34	
4.90/2.34	6:	T:
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)           evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)           evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)           evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)           evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)           evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)           evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)           evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)           evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: ar_1 + 1, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.34	
4.90/2.34			(Comp: 2, Cost: 1)           evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
4.90/2.34	
4.90/2.34			(Comp: ar_1, Cost: 1)        evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
4.90/2.34	
4.90/2.34			(Comp: ?, Cost: 1)           evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
4.90/2.34	
4.90/2.34			(Comp: ar_1, Cost: 1)        evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
4.90/2.34	
4.90/2.34			(Comp: 2, Cost: 1)           evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.90/2.34	
4.90/2.34		start location:	koat_start
4.90/2.34	
4.90/2.34		leaf cost:	0
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Repeatedly propagating knowledge in problem 6 produces the following problem:
4.90/2.34	
4.90/2.34	7:	T:
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)             evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)             evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)             evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)             evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)             evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)             evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)             evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 1)             evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, 1, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: ar_1 + 1, Cost: 1)      evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
4.90/2.34	
4.90/2.34			(Comp: 2, Cost: 1)             evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
4.90/2.34	
4.90/2.34			(Comp: ar_1, Cost: 1)          evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
4.90/2.34	
4.90/2.34			(Comp: 2*ar_1 + 1, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
4.90/2.34	
4.90/2.34			(Comp: ar_1, Cost: 1)          evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
4.90/2.34	
4.90/2.34			(Comp: 2, Cost: 1)             evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.34	
4.90/2.34			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.90/2.34	
4.90/2.34		start location:	koat_start
4.90/2.34	
4.90/2.34		leaf cost:	0
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Complexity upper bound 5*ar_1 + 14
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Time: 0.165 sec (SMT: 0.124 sec)
4.90/2.34	
4.90/2.34	
4.90/2.34	----------------------------------------
4.90/2.34	
4.90/2.34	(2)
4.90/2.34	BOUNDS(1, n^1)
4.90/2.34	
4.90/2.34	----------------------------------------
4.90/2.34	
4.90/2.34	(3) Loat Proof (FINISHED)
4.90/2.34	
4.90/2.34	
4.90/2.34	### Pre-processing the ITS problem ###
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Initial linear ITS problem
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	      0: evalstartstart -> evalstartbb0in : [], cost: 1
4.90/2.34	
4.90/2.34	      1: evalstartbb0in -> evalstart0 : [], cost: 1
4.90/2.34	
4.90/2.34	      2: evalstart0 -> evalstart1 : [], cost: 1
4.90/2.34	
4.90/2.34	      3: evalstart1 -> evalstart2 : [], cost: 1
4.90/2.34	
4.90/2.34	      4: evalstart2 -> evalstart3 : [], cost: 1
4.90/2.34	
4.90/2.34	      5: evalstart3 -> evalstart4 : [], cost: 1
4.90/2.34	
4.90/2.34	      6: evalstart4 -> evalstart5 : [], cost: 1
4.90/2.34	
4.90/2.34	      7: evalstart5 -> evalstartbb1in : A'=B, C'=1, [], cost: 1
4.90/2.34	
4.90/2.34	      8: evalstartbb1in -> evalstartbb2in : D'=A, E'=0, [ C>=1 ], cost: 1
4.90/2.34	
4.90/2.34	      9: evalstartbb1in -> evalstartbb4in : [ 0>=C ], cost: 1
4.90/2.34	
4.90/2.34	     10: evalstartbb2in -> evalstartbb3in : [ D>=1 ], cost: 1
4.90/2.34	
4.90/2.34	     11: evalstartbb2in -> evalstartbb1in : A'=D, C'=E, [ 0>=D ], cost: 1
4.90/2.34	
4.90/2.34	     12: evalstartbb3in -> evalstartbb2in : D'=-1+D, E'=1, [], cost: 1
4.90/2.34	
4.90/2.34	     13: evalstartbb4in -> evalstartstop : [], cost: 1
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Removed unreachable and leaf rules:
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	      0: evalstartstart -> evalstartbb0in : [], cost: 1
4.90/2.34	
4.90/2.34	      1: evalstartbb0in -> evalstart0 : [], cost: 1
4.90/2.34	
4.90/2.34	      2: evalstart0 -> evalstart1 : [], cost: 1
4.90/2.34	
4.90/2.34	      3: evalstart1 -> evalstart2 : [], cost: 1
4.90/2.34	
4.90/2.34	      4: evalstart2 -> evalstart3 : [], cost: 1
4.90/2.34	
4.90/2.34	      5: evalstart3 -> evalstart4 : [], cost: 1
4.90/2.34	
4.90/2.34	      6: evalstart4 -> evalstart5 : [], cost: 1
4.90/2.34	
4.90/2.34	      7: evalstart5 -> evalstartbb1in : A'=B, C'=1, [], cost: 1
4.90/2.34	
4.90/2.34	      8: evalstartbb1in -> evalstartbb2in : D'=A, E'=0, [ C>=1 ], cost: 1
4.90/2.34	
4.90/2.34	     10: evalstartbb2in -> evalstartbb3in : [ D>=1 ], cost: 1
4.90/2.34	
4.90/2.34	     11: evalstartbb2in -> evalstartbb1in : A'=D, C'=E, [ 0>=D ], cost: 1
4.90/2.34	
4.90/2.34	     12: evalstartbb3in -> evalstartbb2in : D'=-1+D, E'=1, [], cost: 1
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	### Simplification by acceleration and chaining ###
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Eliminated locations (on linear paths):
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	     20: evalstartstart -> evalstartbb1in : A'=B, C'=1, [], cost: 8
4.90/2.34	
4.90/2.34	      8: evalstartbb1in -> evalstartbb2in : D'=A, E'=0, [ C>=1 ], cost: 1
4.90/2.34	
4.90/2.34	     11: evalstartbb2in -> evalstartbb1in : A'=D, C'=E, [ 0>=D ], cost: 1
4.90/2.34	
4.90/2.34	     21: evalstartbb2in -> evalstartbb2in : D'=-1+D, E'=1, [ D>=1 ], cost: 2
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Accelerating simple loops of location 9.
4.90/2.34	
4.90/2.34	   Accelerating the following rules:
4.90/2.34	
4.90/2.34	     21: evalstartbb2in -> evalstartbb2in : D'=-1+D, E'=1, [ D>=1 ], cost: 2
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	   Accelerated rule 21 with metering function D, yielding the new rule 22.
4.90/2.34	
4.90/2.34	   Removing the simple loops: 21.
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Accelerated all simple loops using metering functions (where possible):
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	     20: evalstartstart -> evalstartbb1in : A'=B, C'=1, [], cost: 8
4.90/2.34	
4.90/2.34	      8: evalstartbb1in -> evalstartbb2in : D'=A, E'=0, [ C>=1 ], cost: 1
4.90/2.34	
4.90/2.34	     11: evalstartbb2in -> evalstartbb1in : A'=D, C'=E, [ 0>=D ], cost: 1
4.90/2.34	
4.90/2.34	     22: evalstartbb2in -> evalstartbb2in : D'=0, E'=1, [ D>=1 ], cost: 2*D
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Chained accelerated rules (with incoming rules):
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	     20: evalstartstart -> evalstartbb1in : A'=B, C'=1, [], cost: 8
4.90/2.34	
4.90/2.34	      8: evalstartbb1in -> evalstartbb2in : D'=A, E'=0, [ C>=1 ], cost: 1
4.90/2.34	
4.90/2.34	     23: evalstartbb1in -> evalstartbb2in : D'=0, E'=1, [ C>=1 && A>=1 ], cost: 1+2*A
4.90/2.34	
4.90/2.34	     11: evalstartbb2in -> evalstartbb1in : A'=D, C'=E, [ 0>=D ], cost: 1
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Eliminated locations (on tree-shaped paths):
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	     20: evalstartstart -> evalstartbb1in : A'=B, C'=1, [], cost: 8
4.90/2.34	
4.90/2.34	     24: evalstartbb1in -> evalstartbb1in : A'=A, C'=0, D'=A, E'=0, [ C>=1 && 0>=A ], cost: 2
4.90/2.34	
4.90/2.34	     25: evalstartbb1in -> evalstartbb1in : A'=0, C'=1, D'=0, E'=1, [ C>=1 && A>=1 ], cost: 2+2*A
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Accelerating simple loops of location 8.
4.90/2.34	
4.90/2.34	   Simplified some of the simple loops (and removed duplicate rules).
4.90/2.34	
4.90/2.34	   Accelerating the following rules:
4.90/2.34	
4.90/2.34	     24: evalstartbb1in -> evalstartbb1in : C'=0, D'=A, E'=0, [ C>=1 && 0>=A ], cost: 2
4.90/2.34	
4.90/2.34	     25: evalstartbb1in -> evalstartbb1in : A'=0, C'=1, D'=0, E'=1, [ C>=1 && A>=1 ], cost: 2+2*A
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	   Found no metering function for rule 24.
4.90/2.34	
4.90/2.34	   Found no metering function for rule 25.
4.90/2.34	
4.90/2.34	   Removing the simple loops:.
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Accelerated all simple loops using metering functions (where possible):
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	     20: evalstartstart -> evalstartbb1in : A'=B, C'=1, [], cost: 8
4.90/2.34	
4.90/2.34	     24: evalstartbb1in -> evalstartbb1in : C'=0, D'=A, E'=0, [ C>=1 && 0>=A ], cost: 2
4.90/2.34	
4.90/2.34	     25: evalstartbb1in -> evalstartbb1in : A'=0, C'=1, D'=0, E'=1, [ C>=1 && A>=1 ], cost: 2+2*A
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Chained accelerated rules (with incoming rules):
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	     20: evalstartstart -> evalstartbb1in : A'=B, C'=1, [], cost: 8
4.90/2.34	
4.90/2.34	     26: evalstartstart -> evalstartbb1in : A'=B, C'=0, D'=B, E'=0, [ 0>=B ], cost: 10
4.90/2.34	
4.90/2.34	     27: evalstartstart -> evalstartbb1in : A'=0, C'=1, D'=0, E'=1, [ B>=1 ], cost: 10+2*B
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Removed unreachable locations (and leaf rules with constant cost):
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	     27: evalstartstart -> evalstartbb1in : A'=0, C'=1, D'=0, E'=1, [ B>=1 ], cost: 10+2*B
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	### Computing asymptotic complexity ###
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Fully simplified ITS problem
4.90/2.34	
4.90/2.34	   Start location: evalstartstart
4.90/2.34	
4.90/2.34	     27: evalstartstart -> evalstartbb1in : A'=0, C'=1, D'=0, E'=1, [ B>=1 ], cost: 10+2*B
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Computing asymptotic complexity for rule 27
4.90/2.34	
4.90/2.34	   Solved the limit problem by the following transformations:
4.90/2.34	
4.90/2.34	      Created initial limit problem:
4.90/2.34	
4.90/2.34	      10+2*B (+), B (+/+!) [not solved]
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	      removing all constraints (solved by SMT)
4.90/2.34	
4.90/2.34	      resulting limit problem: [solved]
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	      applying transformation rule (C) using substitution {B==n}
4.90/2.34	
4.90/2.34	      resulting limit problem:
4.90/2.34	
4.90/2.34	      [solved]
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	   Solution:
4.90/2.34	
4.90/2.34	      B / n
4.90/2.34	
4.90/2.34	   Resulting cost 10+2*n has complexity: Poly(n^1)
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Found new complexity Poly(n^1).
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	Obtained the following overall complexity (w.r.t. the length of the input n):
4.90/2.34	
4.90/2.34	   Complexity:  Poly(n^1)
4.90/2.34	
4.90/2.34	   Cpx degree:  1
4.90/2.34	
4.90/2.34	   Solved cost: 10+2*n
4.90/2.34	
4.90/2.34	   Rule cost:   10+2*B
4.90/2.34	
4.90/2.34	   Rule guard:  [ B>=1 ]
4.90/2.34	
4.90/2.34	
4.90/2.34	
4.90/2.34	WORST_CASE(Omega(n^1),?)
4.90/2.34	
4.90/2.34	
4.90/2.34	----------------------------------------
4.90/2.34	
4.90/2.34	(4)
4.90/2.34	BOUNDS(n^1, INF)
5.01/2.36	EOF