4.90/2.26	WORST_CASE(Omega(n^1), O(n^1))
4.90/2.27	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.90/2.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.90/2.27	
4.90/2.27	
4.90/2.27	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.90/2.27	
4.90/2.27	(0) CpxIntTrs
4.90/2.27	(1) Koat Proof [FINISHED, 214 ms]
4.90/2.27	(2) BOUNDS(1, n^1)
4.90/2.27	(3) Loat Proof [FINISHED, 630 ms]
4.90/2.27	(4) BOUNDS(n^1, INF)
4.90/2.27	
4.90/2.27	
4.90/2.27	----------------------------------------
4.90/2.27	
4.90/2.27	(0)
4.90/2.27	Obligation:
4.90/2.27	Complexity Int TRS consisting of the following rules:
4.90/2.27	eval_start_start(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb0_in(v__0, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_bb0_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_0(v__0, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_0(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_1(v__0, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_1(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_2(v__0, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_2(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_3(v__0, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_3(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb1_in(v_i, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_bb1_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb2_in(v__0, v__1, v_3, v_i, v_k)) :|: v__0 > 100
4.90/2.27	eval_start_bb1_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb3_in(v__0, v__1, v_3, v_i, v_k)) :|: v__0 <= 100
4.90/2.27	eval_start_bb2_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb1_in(v__0 - 1, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_bb3_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_8(v__0, v__1, v__0 + v_k + 50, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_8(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_9(v__0, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_9(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_10(v__0, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_10(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb4_in(v__0, v_3, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_bb4_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb5_in(v__0, v__1, v_3, v_i, v_k)) :|: v__1 >= 0
4.90/2.27	eval_start_bb4_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb6_in(v__0, v__1, v_3, v_i, v_k)) :|: v__1 < 0
4.90/2.27	eval_start_bb5_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_bb4_in(v__0, v__1 - 1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	eval_start_bb6_in(v__0, v__1, v_3, v_i, v_k) -> Com_1(eval_start_stop(v__0, v__1, v_3, v_i, v_k)) :|: TRUE
4.90/2.27	
4.90/2.27	The start-symbols are:[eval_start_start_5]
4.90/2.27	
4.90/2.27	
4.90/2.27	----------------------------------------
4.90/2.27	
4.90/2.27	(1) Koat Proof (FINISHED)
4.90/2.27	YES(?, 2*ar_1 + 2*ar_3 + 357)
4.90/2.27	
4.90/2.27	
4.90/2.27	
4.90/2.27	Initial complexity problem:
4.90/2.27	
4.90/2.27	1:	T:
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 100 >= ar_0 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_2))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(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 ]
4.90/2.27	
4.90/2.27		start location:	koat_start
4.90/2.27	
4.90/2.27		leaf cost:	0
4.90/2.27	
4.90/2.27	
4.90/2.27	
4.90/2.27	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.90/2.27	
4.90/2.27	2:	T:
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 100 >= ar_0 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_2))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(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 ]
4.90/2.27	
4.90/2.27		start location:	koat_start
4.90/2.27	
4.90/2.27		leaf cost:	0
4.90/2.27	
4.90/2.27	
4.90/2.27	
4.90/2.27	A polynomial rank function with
4.90/2.27	
4.90/2.27		Pol(evalstartstart) = 7
4.90/2.27	
4.90/2.27		Pol(evalstartbb0in) = 7
4.90/2.27	
4.90/2.27		Pol(evalstart0) = 7
4.90/2.27	
4.90/2.27		Pol(evalstart1) = 7
4.90/2.27	
4.90/2.27		Pol(evalstart2) = 7
4.90/2.27	
4.90/2.27		Pol(evalstart3) = 7
4.90/2.27	
4.90/2.27		Pol(evalstartbb1in) = 7
4.90/2.27	
4.90/2.27		Pol(evalstartbb2in) = 7
4.90/2.27	
4.90/2.27		Pol(evalstartbb3in) = 6
4.90/2.27	
4.90/2.27		Pol(evalstart8) = 5
4.90/2.27	
4.90/2.27		Pol(evalstart9) = 4
4.90/2.27	
4.90/2.27		Pol(evalstart10) = 3
4.90/2.27	
4.90/2.27		Pol(evalstartbb4in) = 2
4.90/2.27	
4.90/2.27		Pol(evalstartbb5in) = 2
4.90/2.27	
4.90/2.27		Pol(evalstartbb6in) = 1
4.90/2.27	
4.90/2.27		Pol(evalstartstop) = 0
4.90/2.27	
4.90/2.27		Pol(koat_start) = 7
4.90/2.27	
4.90/2.27	orients all transitions weakly and the transitions
4.90/2.27	
4.90/2.27		evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27		evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ]
4.90/2.27	
4.90/2.27		evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3, ar_4))
4.90/2.27	
4.90/2.27		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 100 >= ar_0 ]
4.90/2.27	
4.90/2.27		evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27		evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27		evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_2))
4.90/2.27	
4.90/2.27	strictly and produces the following problem:
4.90/2.27	
4.90/2.27	3:	T:
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(Comp: 1, Cost: 1)    evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 100 >= ar_0 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)    evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)    evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)    evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)    evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_2))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)    evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(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 ]
4.90/2.27	
4.90/2.27		start location:	koat_start
4.90/2.27	
4.90/2.27		leaf cost:	0
4.90/2.27	
4.90/2.27	
4.90/2.27	
4.90/2.27	A polynomial rank function with
4.90/2.27	
4.90/2.27		Pol(evalstartstart) = V_2
4.90/2.27	
4.90/2.27		Pol(evalstartbb0in) = V_2
4.90/2.27	
4.90/2.27		Pol(evalstart0) = V_2
4.90/2.27	
4.90/2.27		Pol(evalstart1) = V_2
4.90/2.27	
4.90/2.27		Pol(evalstart2) = V_2
4.90/2.27	
4.90/2.27		Pol(evalstart3) = V_2
4.90/2.27	
4.90/2.27		Pol(evalstartbb1in) = V_1
4.90/2.27	
4.90/2.27		Pol(evalstartbb2in) = V_1 - 1
4.90/2.27	
4.90/2.27		Pol(evalstartbb3in) = V_1
4.90/2.27	
4.90/2.27		Pol(evalstart8) = V_1
4.90/2.27	
4.90/2.27		Pol(evalstart9) = V_1
4.90/2.27	
4.90/2.27		Pol(evalstart10) = V_1
4.90/2.27	
4.90/2.27		Pol(evalstartbb4in) = V_1
4.90/2.27	
4.90/2.27		Pol(evalstartbb5in) = V_1
4.90/2.27	
4.90/2.27		Pol(evalstartbb6in) = V_1
4.90/2.27	
4.90/2.27		Pol(evalstartstop) = V_1
4.90/2.27	
4.90/2.27		Pol(koat_start) = V_2
4.90/2.27	
4.90/2.27	orients all transitions weakly and the transition
4.90/2.27	
4.90/2.27		evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 ]
4.90/2.27	
4.90/2.27	strictly and produces the following problem:
4.90/2.27	
4.90/2.27	4:	T:
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(Comp: 1, Cost: 1)       evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ar_1, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 100 >= ar_0 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)       evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_2))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)       evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)       evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(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 ]
4.90/2.27	
4.90/2.27		start location:	koat_start
4.90/2.27	
4.90/2.27		leaf cost:	0
4.90/2.27	
4.90/2.27	
4.90/2.27	
4.90/2.27	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.90/2.27	
4.90/2.27	5:	T:
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(Comp: 1, Cost: 1)       evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ar_1, Cost: 1)    evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 100 >= ar_0 ]
4.90/2.27	
4.90/2.27			(Comp: ar_1, Cost: 1)    evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_2))
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)       evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)       evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)       evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(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 ]
4.90/2.27	
4.90/2.27		start location:	koat_start
4.90/2.27	
4.90/2.27		leaf cost:	0
4.90/2.27	
4.90/2.27	
4.90/2.27	
4.90/2.27	A polynomial rank function with
4.90/2.27	
4.90/2.27		Pol(evalstartstart) = V_4 + 151
4.90/2.27	
4.90/2.27		Pol(evalstartbb0in) = V_4 + 151
4.90/2.27	
4.90/2.27		Pol(evalstart0) = V_4 + 151
4.90/2.27	
4.90/2.27		Pol(evalstart1) = V_4 + 151
4.90/2.27	
4.90/2.27		Pol(evalstart2) = V_4 + 151
4.90/2.27	
4.90/2.27		Pol(evalstart3) = V_4 + 151
4.90/2.27	
4.90/2.27		Pol(evalstartbb1in) = V_4 + 151
4.90/2.27	
4.90/2.27		Pol(evalstartbb2in) = V_4 + 151
4.90/2.27	
4.90/2.27		Pol(evalstartbb3in) = V_1 + V_4 + 51
4.90/2.27	
4.90/2.27		Pol(evalstart8) = V_3 + 1
4.90/2.27	
4.90/2.27		Pol(evalstart9) = V_3 + 1
4.90/2.27	
4.90/2.27		Pol(evalstart10) = V_3 + 1
4.90/2.27	
4.90/2.27		Pol(evalstartbb4in) = V_5 + 1
4.90/2.27	
4.90/2.27		Pol(evalstartbb5in) = V_5
4.90/2.27	
4.90/2.27		Pol(evalstartbb6in) = V_5
4.90/2.27	
4.90/2.27		Pol(evalstartstop) = V_5
4.90/2.27	
4.90/2.27		Pol(koat_start) = V_4 + 151
4.90/2.27	
4.90/2.27	orients all transitions weakly and the transition
4.90/2.27	
4.90/2.27		evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 ]
4.90/2.27	
4.90/2.27	strictly and produces the following problem:
4.90/2.27	
4.90/2.27	6:	T:
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(Comp: 1, Cost: 1)             evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ar_1, Cost: 1)          evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 100 >= ar_0 ]
4.90/2.27	
4.90/2.27			(Comp: ar_1, Cost: 1)          evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_2))
4.90/2.27	
4.90/2.27			(Comp: ar_3 + 151, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ]
4.90/2.27	
4.90/2.27			(Comp: ?, Cost: 1)             evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(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 ]
4.90/2.27	
4.90/2.27		start location:	koat_start
4.90/2.27	
4.90/2.27		leaf cost:	0
4.90/2.27	
4.90/2.27	
4.90/2.27	
4.90/2.27	Repeatedly propagating knowledge in problem 6 produces the following problem:
4.90/2.27	
4.90/2.27	7:	T:
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(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))
4.90/2.27	
4.90/2.27			(Comp: 1, Cost: 1)             evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: ar_1, Cost: 1)          evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 ]
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 100 >= ar_0 ]
4.90/2.27	
4.90/2.27			(Comp: ar_1, Cost: 1)          evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.27	
4.90/2.27			(Comp: 7, Cost: 1)             evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_2))
4.90/2.28	
4.90/2.28			(Comp: ar_3 + 151, Cost: 1)    evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 ]
4.90/2.28	
4.90/2.28			(Comp: 7, Cost: 1)             evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ]
4.90/2.28	
4.90/2.28			(Comp: ar_3 + 151, Cost: 1)    evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1))
4.90/2.28	
4.90/2.28			(Comp: 7, Cost: 1)             evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.90/2.28	
4.90/2.28			(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 ]
4.90/2.28	
4.90/2.28		start location:	koat_start
4.90/2.28	
4.90/2.28		leaf cost:	0
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Complexity upper bound 2*ar_1 + 2*ar_3 + 357
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Time: 0.229 sec (SMT: 0.175 sec)
4.90/2.28	
4.90/2.28	
4.90/2.28	----------------------------------------
4.90/2.28	
4.90/2.28	(2)
4.90/2.28	BOUNDS(1, n^1)
4.90/2.28	
4.90/2.28	----------------------------------------
4.90/2.28	
4.90/2.28	(3) Loat Proof (FINISHED)
4.90/2.28	
4.90/2.28	
4.90/2.28	### Pre-processing the ITS problem ###
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Initial linear ITS problem
4.90/2.28	
4.90/2.28	   Start location: evalstartstart
4.90/2.28	
4.90/2.28	      0: evalstartstart -> evalstartbb0in : [], cost: 1
4.90/2.28	
4.90/2.28	      1: evalstartbb0in -> evalstart0 : [], cost: 1
4.90/2.28	
4.90/2.28	      2: evalstart0 -> evalstart1 : [], cost: 1
4.90/2.28	
4.90/2.28	      3: evalstart1 -> evalstart2 : [], cost: 1
4.90/2.28	
4.90/2.28	      4: evalstart2 -> evalstart3 : [], cost: 1
4.90/2.28	
4.90/2.28	      5: evalstart3 -> evalstartbb1in : A'=B, [], cost: 1
4.90/2.28	
4.90/2.28	      6: evalstartbb1in -> evalstartbb2in : [ A>=101 ], cost: 1
4.90/2.28	
4.90/2.28	      7: evalstartbb1in -> evalstartbb3in : [ 100>=A ], cost: 1
4.90/2.28	
4.90/2.28	      8: evalstartbb2in -> evalstartbb1in : A'=-1+A, [], cost: 1
4.90/2.28	
4.90/2.28	      9: evalstartbb3in -> evalstart8 : C'=50+D+A, [], cost: 1
4.90/2.28	
4.90/2.28	     10: evalstart8 -> evalstart9 : [], cost: 1
4.90/2.28	
4.90/2.28	     11: evalstart9 -> evalstart10 : [], cost: 1
4.90/2.28	
4.90/2.28	     12: evalstart10 -> evalstartbb4in : E'=C, [], cost: 1
4.90/2.28	
4.90/2.28	     13: evalstartbb4in -> evalstartbb5in : [ E>=0 ], cost: 1
4.90/2.28	
4.90/2.28	     14: evalstartbb4in -> evalstartbb6in : [ 0>=1+E ], cost: 1
4.90/2.28	
4.90/2.28	     15: evalstartbb5in -> evalstartbb4in : E'=-1+E, [], cost: 1
4.90/2.28	
4.90/2.28	     16: evalstartbb6in -> evalstartstop : [], cost: 1
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Removed unreachable and leaf rules:
4.90/2.28	
4.90/2.28	   Start location: evalstartstart
4.90/2.28	
4.90/2.28	      0: evalstartstart -> evalstartbb0in : [], cost: 1
4.90/2.28	
4.90/2.28	      1: evalstartbb0in -> evalstart0 : [], cost: 1
4.90/2.28	
4.90/2.28	      2: evalstart0 -> evalstart1 : [], cost: 1
4.90/2.28	
4.90/2.28	      3: evalstart1 -> evalstart2 : [], cost: 1
4.90/2.28	
4.90/2.28	      4: evalstart2 -> evalstart3 : [], cost: 1
4.90/2.28	
4.90/2.28	      5: evalstart3 -> evalstartbb1in : A'=B, [], cost: 1
4.90/2.28	
4.90/2.28	      6: evalstartbb1in -> evalstartbb2in : [ A>=101 ], cost: 1
4.90/2.28	
4.90/2.28	      7: evalstartbb1in -> evalstartbb3in : [ 100>=A ], cost: 1
4.90/2.28	
4.90/2.28	      8: evalstartbb2in -> evalstartbb1in : A'=-1+A, [], cost: 1
4.90/2.28	
4.90/2.28	      9: evalstartbb3in -> evalstart8 : C'=50+D+A, [], cost: 1
4.90/2.28	
4.90/2.28	     10: evalstart8 -> evalstart9 : [], cost: 1
4.90/2.28	
4.90/2.28	     11: evalstart9 -> evalstart10 : [], cost: 1
4.90/2.28	
4.90/2.28	     12: evalstart10 -> evalstartbb4in : E'=C, [], cost: 1
4.90/2.28	
4.90/2.28	     13: evalstartbb4in -> evalstartbb5in : [ E>=0 ], cost: 1
4.90/2.28	
4.90/2.28	     15: evalstartbb5in -> evalstartbb4in : E'=-1+E, [], cost: 1
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	### Simplification by acceleration and chaining ###
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Eliminated locations (on linear paths):
4.90/2.28	
4.90/2.28	   Start location: evalstartstart
4.90/2.28	
4.90/2.28	     21: evalstartstart -> evalstartbb1in : A'=B, [], cost: 6
4.90/2.28	
4.90/2.28	     22: evalstartbb1in -> evalstartbb1in : A'=-1+A, [ A>=101 ], cost: 2
4.90/2.28	
4.90/2.28	     26: evalstartbb1in -> evalstartbb4in : C'=50+D+A, E'=50+D+A, [ 100>=A ], cost: 5
4.90/2.28	
4.90/2.28	     27: evalstartbb4in -> evalstartbb4in : E'=-1+E, [ E>=0 ], cost: 2
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Accelerating simple loops of location 6.
4.90/2.28	
4.90/2.28	   Accelerating the following rules:
4.90/2.28	
4.90/2.28	     22: evalstartbb1in -> evalstartbb1in : A'=-1+A, [ A>=101 ], cost: 2
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	   Accelerated rule 22 with metering function -100+A, yielding the new rule 28.
4.90/2.28	
4.90/2.28	   Removing the simple loops: 22.
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Accelerating simple loops of location 12.
4.90/2.28	
4.90/2.28	   Accelerating the following rules:
4.90/2.28	
4.90/2.28	     27: evalstartbb4in -> evalstartbb4in : E'=-1+E, [ E>=0 ], cost: 2
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	   Accelerated rule 27 with metering function 1+E, yielding the new rule 29.
4.90/2.28	
4.90/2.28	   Removing the simple loops: 27.
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Accelerated all simple loops using metering functions (where possible):
4.90/2.28	
4.90/2.28	   Start location: evalstartstart
4.90/2.28	
4.90/2.28	     21: evalstartstart -> evalstartbb1in : A'=B, [], cost: 6
4.90/2.28	
4.90/2.28	     26: evalstartbb1in -> evalstartbb4in : C'=50+D+A, E'=50+D+A, [ 100>=A ], cost: 5
4.90/2.28	
4.90/2.28	     28: evalstartbb1in -> evalstartbb1in : A'=100, [ A>=101 ], cost: -200+2*A
4.90/2.28	
4.90/2.28	     29: evalstartbb4in -> evalstartbb4in : E'=-1, [ E>=0 ], cost: 2+2*E
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Chained accelerated rules (with incoming rules):
4.90/2.28	
4.90/2.28	   Start location: evalstartstart
4.90/2.28	
4.90/2.28	     21: evalstartstart -> evalstartbb1in : A'=B, [], cost: 6
4.90/2.28	
4.90/2.28	     30: evalstartstart -> evalstartbb1in : A'=100, [ B>=101 ], cost: -194+2*B
4.90/2.28	
4.90/2.28	     26: evalstartbb1in -> evalstartbb4in : C'=50+D+A, E'=50+D+A, [ 100>=A ], cost: 5
4.90/2.28	
4.90/2.28	     31: evalstartbb1in -> evalstartbb4in : C'=50+D+A, E'=-1, [ 100>=A && 50+D+A>=0 ], cost: 107+2*D+2*A
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Removed unreachable locations (and leaf rules with constant cost):
4.90/2.28	
4.90/2.28	   Start location: evalstartstart
4.90/2.28	
4.90/2.28	     21: evalstartstart -> evalstartbb1in : A'=B, [], cost: 6
4.90/2.28	
4.90/2.28	     30: evalstartstart -> evalstartbb1in : A'=100, [ B>=101 ], cost: -194+2*B
4.90/2.28	
4.90/2.28	     31: evalstartbb1in -> evalstartbb4in : C'=50+D+A, E'=-1, [ 100>=A && 50+D+A>=0 ], cost: 107+2*D+2*A
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Eliminated locations (on tree-shaped paths):
4.90/2.28	
4.90/2.28	   Start location: evalstartstart
4.90/2.28	
4.90/2.28	     32: evalstartstart -> evalstartbb4in : A'=B, C'=50+D+B, E'=-1, [ 100>=B && 50+D+B>=0 ], cost: 113+2*D+2*B
4.90/2.28	
4.90/2.28	     33: evalstartstart -> evalstartbb4in : A'=100, C'=150+D, E'=-1, [ B>=101 && 150+D>=0 ], cost: 113+2*D+2*B
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	### Computing asymptotic complexity ###
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Fully simplified ITS problem
4.90/2.28	
4.90/2.28	   Start location: evalstartstart
4.90/2.28	
4.90/2.28	     32: evalstartstart -> evalstartbb4in : A'=B, C'=50+D+B, E'=-1, [ 100>=B && 50+D+B>=0 ], cost: 113+2*D+2*B
4.90/2.28	
4.90/2.28	     33: evalstartstart -> evalstartbb4in : A'=100, C'=150+D, E'=-1, [ B>=101 && 150+D>=0 ], cost: 113+2*D+2*B
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Computing asymptotic complexity for rule 32
4.90/2.28	
4.90/2.28	   Solved the limit problem by the following transformations:
4.90/2.28	
4.90/2.28	      Created initial limit problem:
4.90/2.28	
4.90/2.28	      113+2*D+2*B (+), 51+D+B (+/+!), 101-B (+/+!) [not solved]
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	      applying transformation rule (C) using substitution {B==100}
4.90/2.28	
4.90/2.28	      resulting limit problem:
4.90/2.28	
4.90/2.28	      1 (+/+!), 151+D (+/+!), 313+2*D (+) [not solved]
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	      applying transformation rule (B), deleting 1 (+/+!)
4.90/2.28	
4.90/2.28	      resulting limit problem:
4.90/2.28	
4.90/2.28	      151+D (+/+!), 313+2*D (+) [not solved]
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	      removing all constraints (solved by SMT)
4.90/2.28	
4.90/2.28	      resulting limit problem: [solved]
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	      applying transformation rule (C) using substitution {D==n}
4.90/2.28	
4.90/2.28	      resulting limit problem:
4.90/2.28	
4.90/2.28	      [solved]
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	   Solution:
4.90/2.28	
4.90/2.28	      D / n
4.90/2.28	
4.90/2.28	      B / 100
4.90/2.28	
4.90/2.28	   Resulting cost 313+2*n has complexity: Poly(n^1)
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Found new complexity Poly(n^1).
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	Obtained the following overall complexity (w.r.t. the length of the input n):
4.90/2.28	
4.90/2.28	   Complexity:  Poly(n^1)
4.90/2.28	
4.90/2.28	   Cpx degree:  1
4.90/2.28	
4.90/2.28	   Solved cost: 313+2*n
4.90/2.28	
4.90/2.28	   Rule cost:   113+2*D+2*B
4.90/2.28	
4.90/2.28	   Rule guard:  [ 100>=B && 50+D+B>=0 ]
4.90/2.28	
4.90/2.28	
4.90/2.28	
4.90/2.28	WORST_CASE(Omega(n^1),?)
4.90/2.28	
4.90/2.28	
4.90/2.28	----------------------------------------
4.90/2.28	
4.90/2.28	(4)
4.90/2.28	BOUNDS(n^1, INF)
4.99/2.31	EOF