4.56/2.14	WORST_CASE(Omega(n^1), O(n^1))
4.56/2.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.56/2.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.56/2.15	
4.56/2.15	
4.56/2.15	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.56/2.15	
4.56/2.15	(0) CpxIntTrs
4.56/2.15	(1) Koat Proof [FINISHED, 24 ms]
4.56/2.15	(2) BOUNDS(1, n^1)
4.56/2.15	(3) Loat Proof [FINISHED, 414 ms]
4.56/2.15	(4) BOUNDS(n^1, INF)
4.56/2.15	
4.56/2.15	
4.56/2.15	----------------------------------------
4.56/2.15	
4.56/2.15	(0)
4.56/2.15	Obligation:
4.56/2.15	Complexity Int TRS consisting of the following rules:
4.56/2.15	eval_speedSingleSingle_start(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_bb0_in(v_n, v_x_0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_bb0_in(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_0(v_n, v_x_0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_0(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_1(v_n, v_x_0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_1(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_2(v_n, v_x_0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_2(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_3(v_n, v_x_0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_3(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_4(v_n, v_x_0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_4(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_bb1_in(v_n, 0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_bb1_in(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_bb2_in(v_n, v_x_0)) :|: v_x_0 < v_n
4.56/2.15	eval_speedSingleSingle_bb1_in(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_bb3_in(v_n, v_x_0)) :|: v_x_0 >= v_n
4.56/2.15	eval_speedSingleSingle_bb2_in(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_5(v_n, v_x_0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_5(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_6(v_n, v_x_0)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_6(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_bb1_in(v_n, v_x_0 + 1)) :|: TRUE
4.56/2.15	eval_speedSingleSingle_bb3_in(v_n, v_x_0) -> Com_1(eval_speedSingleSingle_stop(v_n, v_x_0)) :|: TRUE
4.56/2.15	
4.56/2.15	The start-symbols are:[eval_speedSingleSingle_start_2]
4.56/2.15	
4.56/2.15	
4.56/2.15	----------------------------------------
4.56/2.15	
4.56/2.15	(1) Koat Proof (FINISHED)
4.56/2.15	YES(?, 4*ar_1 + 15)
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Initial complexity problem:
4.56/2.15	
4.56/2.15	1:	T:
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglestart(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb0in(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb0in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle0(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle0(ar_0, ar_1) -> Com_1(evalspeedSingleSingle1(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle1(ar_0, ar_1) -> Com_1(evalspeedSingleSingle2(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle2(ar_0, ar_1) -> Com_1(evalspeedSingleSingle3(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle3(ar_0, ar_1) -> Com_1(evalspeedSingleSingle4(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle4(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb2in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle5(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle5(ar_0, ar_1) -> Com_1(evalspeedSingleSingle6(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle6(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(ar_0 + 1, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb3in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestop(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestart(ar_0, ar_1)) [ 0 <= 0 ]
4.56/2.15	
4.56/2.15		start location:	koat_start
4.56/2.15	
4.56/2.15		leaf cost:	0
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.56/2.15	
4.56/2.15	2:	T:
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSinglestart(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb0in(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSinglebb0in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle0(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle0(ar_0, ar_1) -> Com_1(evalspeedSingleSingle1(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle1(ar_0, ar_1) -> Com_1(evalspeedSingleSingle2(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle2(ar_0, ar_1) -> Com_1(evalspeedSingleSingle3(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle3(ar_0, ar_1) -> Com_1(evalspeedSingleSingle4(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle4(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb2in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle5(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle5(ar_0, ar_1) -> Com_1(evalspeedSingleSingle6(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle6(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(ar_0 + 1, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb3in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestop(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestart(ar_0, ar_1)) [ 0 <= 0 ]
4.56/2.15	
4.56/2.15		start location:	koat_start
4.56/2.15	
4.56/2.15		leaf cost:	0
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	A polynomial rank function with
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglestart) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglebb0in) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle0) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle1) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle2) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle3) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle4) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglebb1in) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglebb2in) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglebb3in) = 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle5) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle6) = 2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglestop) = 0
4.56/2.15	
4.56/2.15		Pol(koat_start) = 2
4.56/2.15	
4.56/2.15	orients all transitions weakly and the transitions
4.56/2.15	
4.56/2.15		evalspeedSingleSinglebb3in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestop(ar_0, ar_1))
4.56/2.15	
4.56/2.15		evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
4.56/2.15	
4.56/2.15	strictly and produces the following problem:
4.56/2.15	
4.56/2.15	3:	T:
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSinglestart(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb0in(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSinglebb0in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle0(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle0(ar_0, ar_1) -> Com_1(evalspeedSingleSingle1(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle1(ar_0, ar_1) -> Com_1(evalspeedSingleSingle2(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle2(ar_0, ar_1) -> Com_1(evalspeedSingleSingle3(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle3(ar_0, ar_1) -> Com_1(evalspeedSingleSingle4(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)    evalspeedSingleSingle4(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
4.56/2.15	
4.56/2.15			(Comp: 2, Cost: 1)    evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSinglebb2in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle5(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle5(ar_0, ar_1) -> Com_1(evalspeedSingleSingle6(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)    evalspeedSingleSingle6(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(ar_0 + 1, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 2, Cost: 1)    evalspeedSingleSinglebb3in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestop(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestart(ar_0, ar_1)) [ 0 <= 0 ]
4.56/2.15	
4.56/2.15		start location:	koat_start
4.56/2.15	
4.56/2.15		leaf cost:	0
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	A polynomial rank function with
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglestart) = V_2 + 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglebb0in) = V_2 + 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle0) = V_2 + 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle1) = V_2 + 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle2) = V_2 + 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle3) = V_2 + 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle4) = V_2 + 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglebb1in) = -V_1 + V_2 + 1
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglebb2in) = -V_1 + V_2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglebb3in) = -V_1 + V_2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle5) = -V_1 + V_2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSingle6) = -V_1 + V_2
4.56/2.15	
4.56/2.15		Pol(evalspeedSingleSinglestop) = -V_1 + V_2
4.56/2.15	
4.56/2.15		Pol(koat_start) = V_2 + 1
4.56/2.15	
4.56/2.15	orients all transitions weakly and the transition
4.56/2.15	
4.56/2.15		evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
4.56/2.15	
4.56/2.15	strictly and produces the following problem:
4.56/2.15	
4.56/2.15	4:	T:
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSinglestart(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb0in(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSinglebb0in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle0(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle0(ar_0, ar_1) -> Com_1(evalspeedSingleSingle1(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle1(ar_0, ar_1) -> Com_1(evalspeedSingleSingle2(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle2(ar_0, ar_1) -> Com_1(evalspeedSingleSingle3(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle3(ar_0, ar_1) -> Com_1(evalspeedSingleSingle4(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle4(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ar_1 + 1, Cost: 1)    evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
4.56/2.15	
4.56/2.15			(Comp: 2, Cost: 1)           evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)           evalspeedSingleSinglebb2in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle5(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)           evalspeedSingleSingle5(ar_0, ar_1) -> Com_1(evalspeedSingleSingle6(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ?, Cost: 1)           evalspeedSingleSingle6(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(ar_0 + 1, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 2, Cost: 1)           evalspeedSingleSinglebb3in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestop(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestart(ar_0, ar_1)) [ 0 <= 0 ]
4.56/2.15	
4.56/2.15		start location:	koat_start
4.56/2.15	
4.56/2.15		leaf cost:	0
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.56/2.15	
4.56/2.15	5:	T:
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSinglestart(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb0in(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSinglebb0in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle0(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle0(ar_0, ar_1) -> Com_1(evalspeedSingleSingle1(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle1(ar_0, ar_1) -> Com_1(evalspeedSingleSingle2(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle2(ar_0, ar_1) -> Com_1(evalspeedSingleSingle3(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle3(ar_0, ar_1) -> Com_1(evalspeedSingleSingle4(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 1)           evalspeedSingleSingle4(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ar_1 + 1, Cost: 1)    evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb2in(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
4.56/2.15	
4.56/2.15			(Comp: 2, Cost: 1)           evalspeedSingleSinglebb1in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
4.56/2.15	
4.56/2.15			(Comp: ar_1 + 1, Cost: 1)    evalspeedSingleSinglebb2in(ar_0, ar_1) -> Com_1(evalspeedSingleSingle5(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ar_1 + 1, Cost: 1)    evalspeedSingleSingle5(ar_0, ar_1) -> Com_1(evalspeedSingleSingle6(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: ar_1 + 1, Cost: 1)    evalspeedSingleSingle6(ar_0, ar_1) -> Com_1(evalspeedSingleSinglebb1in(ar_0 + 1, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 2, Cost: 1)           evalspeedSingleSinglebb3in(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestop(ar_0, ar_1))
4.56/2.15	
4.56/2.15			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1) -> Com_1(evalspeedSingleSinglestart(ar_0, ar_1)) [ 0 <= 0 ]
4.56/2.15	
4.56/2.15		start location:	koat_start
4.56/2.15	
4.56/2.15		leaf cost:	0
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Complexity upper bound 4*ar_1 + 15
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Time: 0.067 sec (SMT: 0.059 sec)
4.56/2.15	
4.56/2.15	
4.56/2.15	----------------------------------------
4.56/2.15	
4.56/2.15	(2)
4.56/2.15	BOUNDS(1, n^1)
4.56/2.15	
4.56/2.15	----------------------------------------
4.56/2.15	
4.56/2.15	(3) Loat Proof (FINISHED)
4.56/2.15	
4.56/2.15	
4.56/2.15	### Pre-processing the ITS problem ###
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Initial linear ITS problem
4.56/2.15	
4.56/2.15	   Start location: evalspeedSingleSinglestart
4.56/2.15	
4.56/2.15	      0: evalspeedSingleSinglestart -> evalspeedSingleSinglebb0in : [], cost: 1
4.56/2.15	
4.56/2.15	      1: evalspeedSingleSinglebb0in -> evalspeedSingleSingle0 : [], cost: 1
4.56/2.15	
4.56/2.15	      2: evalspeedSingleSingle0 -> evalspeedSingleSingle1 : [], cost: 1
4.56/2.15	
4.56/2.15	      3: evalspeedSingleSingle1 -> evalspeedSingleSingle2 : [], cost: 1
4.56/2.15	
4.56/2.15	      4: evalspeedSingleSingle2 -> evalspeedSingleSingle3 : [], cost: 1
4.56/2.15	
4.56/2.15	      5: evalspeedSingleSingle3 -> evalspeedSingleSingle4 : [], cost: 1
4.56/2.15	
4.56/2.15	      6: evalspeedSingleSingle4 -> evalspeedSingleSinglebb1in : A'=0, [], cost: 1
4.56/2.15	
4.56/2.15	      7: evalspeedSingleSinglebb1in -> evalspeedSingleSinglebb2in : [ B>=1+A ], cost: 1
4.56/2.15	
4.56/2.15	      8: evalspeedSingleSinglebb1in -> evalspeedSingleSinglebb3in : [ A>=B ], cost: 1
4.56/2.15	
4.56/2.15	      9: evalspeedSingleSinglebb2in -> evalspeedSingleSingle5 : [], cost: 1
4.56/2.15	
4.56/2.15	     10: evalspeedSingleSingle5 -> evalspeedSingleSingle6 : [], cost: 1
4.56/2.15	
4.56/2.15	     11: evalspeedSingleSingle6 -> evalspeedSingleSinglebb1in : A'=1+A, [], cost: 1
4.56/2.15	
4.56/2.15	     12: evalspeedSingleSinglebb3in -> evalspeedSingleSinglestop : [], cost: 1
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Removed unreachable and leaf rules:
4.56/2.15	
4.56/2.15	   Start location: evalspeedSingleSinglestart
4.56/2.15	
4.56/2.15	      0: evalspeedSingleSinglestart -> evalspeedSingleSinglebb0in : [], cost: 1
4.56/2.15	
4.56/2.15	      1: evalspeedSingleSinglebb0in -> evalspeedSingleSingle0 : [], cost: 1
4.56/2.15	
4.56/2.15	      2: evalspeedSingleSingle0 -> evalspeedSingleSingle1 : [], cost: 1
4.56/2.15	
4.56/2.15	      3: evalspeedSingleSingle1 -> evalspeedSingleSingle2 : [], cost: 1
4.56/2.15	
4.56/2.15	      4: evalspeedSingleSingle2 -> evalspeedSingleSingle3 : [], cost: 1
4.56/2.15	
4.56/2.15	      5: evalspeedSingleSingle3 -> evalspeedSingleSingle4 : [], cost: 1
4.56/2.15	
4.56/2.15	      6: evalspeedSingleSingle4 -> evalspeedSingleSinglebb1in : A'=0, [], cost: 1
4.56/2.15	
4.56/2.15	      7: evalspeedSingleSinglebb1in -> evalspeedSingleSinglebb2in : [ B>=1+A ], cost: 1
4.56/2.15	
4.56/2.15	      9: evalspeedSingleSinglebb2in -> evalspeedSingleSingle5 : [], cost: 1
4.56/2.15	
4.56/2.15	     10: evalspeedSingleSingle5 -> evalspeedSingleSingle6 : [], cost: 1
4.56/2.15	
4.56/2.15	     11: evalspeedSingleSingle6 -> evalspeedSingleSinglebb1in : A'=1+A, [], cost: 1
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	### Simplification by acceleration and chaining ###
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Eliminated locations (on linear paths):
4.56/2.15	
4.56/2.15	   Start location: evalspeedSingleSinglestart
4.56/2.15	
4.56/2.15	     18: evalspeedSingleSinglestart -> evalspeedSingleSinglebb1in : A'=0, [], cost: 7
4.56/2.15	
4.56/2.15	     21: evalspeedSingleSinglebb1in -> evalspeedSingleSinglebb1in : A'=1+A, [ B>=1+A ], cost: 4
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Accelerating simple loops of location 7.
4.56/2.15	
4.56/2.15	   Accelerating the following rules:
4.56/2.15	
4.56/2.15	     21: evalspeedSingleSinglebb1in -> evalspeedSingleSinglebb1in : A'=1+A, [ B>=1+A ], cost: 4
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	   Accelerated rule 21 with metering function -A+B, yielding the new rule 22.
4.56/2.15	
4.56/2.15	   Removing the simple loops: 21.
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Accelerated all simple loops using metering functions (where possible):
4.56/2.15	
4.56/2.15	   Start location: evalspeedSingleSinglestart
4.56/2.15	
4.56/2.15	     18: evalspeedSingleSinglestart -> evalspeedSingleSinglebb1in : A'=0, [], cost: 7
4.56/2.15	
4.56/2.15	     22: evalspeedSingleSinglebb1in -> evalspeedSingleSinglebb1in : A'=B, [ B>=1+A ], cost: -4*A+4*B
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Chained accelerated rules (with incoming rules):
4.56/2.15	
4.56/2.15	   Start location: evalspeedSingleSinglestart
4.56/2.15	
4.56/2.15	     18: evalspeedSingleSinglestart -> evalspeedSingleSinglebb1in : A'=0, [], cost: 7
4.56/2.15	
4.56/2.15	     23: evalspeedSingleSinglestart -> evalspeedSingleSinglebb1in : A'=B, [ B>=1 ], cost: 7+4*B
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Removed unreachable locations (and leaf rules with constant cost):
4.56/2.15	
4.56/2.15	   Start location: evalspeedSingleSinglestart
4.56/2.15	
4.56/2.15	     23: evalspeedSingleSinglestart -> evalspeedSingleSinglebb1in : A'=B, [ B>=1 ], cost: 7+4*B
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	### Computing asymptotic complexity ###
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Fully simplified ITS problem
4.56/2.15	
4.56/2.15	   Start location: evalspeedSingleSinglestart
4.56/2.15	
4.56/2.15	     23: evalspeedSingleSinglestart -> evalspeedSingleSinglebb1in : A'=B, [ B>=1 ], cost: 7+4*B
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Computing asymptotic complexity for rule 23
4.56/2.15	
4.56/2.15	   Solved the limit problem by the following transformations:
4.56/2.15	
4.56/2.15	      Created initial limit problem:
4.56/2.15	
4.56/2.15	      7+4*B (+), B (+/+!) [not solved]
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	      removing all constraints (solved by SMT)
4.56/2.15	
4.56/2.15	      resulting limit problem: [solved]
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	      applying transformation rule (C) using substitution {B==n}
4.56/2.15	
4.56/2.15	      resulting limit problem:
4.56/2.15	
4.56/2.15	      [solved]
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	   Solution:
4.56/2.15	
4.56/2.15	      B / n
4.56/2.15	
4.56/2.15	   Resulting cost 7+4*n has complexity: Poly(n^1)
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Found new complexity Poly(n^1).
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	Obtained the following overall complexity (w.r.t. the length of the input n):
4.56/2.15	
4.56/2.15	   Complexity:  Poly(n^1)
4.56/2.15	
4.56/2.15	   Cpx degree:  1
4.56/2.15	
4.56/2.15	   Solved cost: 7+4*n
4.56/2.15	
4.56/2.15	   Rule cost:   7+4*B
4.56/2.15	
4.56/2.15	   Rule guard:  [ B>=1 ]
4.56/2.15	
4.56/2.15	
4.56/2.15	
4.56/2.15	WORST_CASE(Omega(n^1),?)
4.56/2.15	
4.56/2.15	
4.56/2.15	----------------------------------------
4.56/2.15	
4.56/2.15	(4)
4.56/2.15	BOUNDS(n^1, INF)
4.56/2.16	EOF