5.53/2.55	WORST_CASE(Omega(n^1), O(n^1))
5.53/2.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.53/2.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.53/2.56	
5.53/2.56	
5.53/2.56	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.53/2.56	
5.53/2.56	(0) CpxIntTrs
5.53/2.56	(1) Koat Proof [FINISHED, 322 ms]
5.53/2.56	(2) BOUNDS(1, n^1)
5.53/2.56	(3) Loat Proof [FINISHED, 819 ms]
5.53/2.56	(4) BOUNDS(n^1, INF)
5.53/2.56	
5.53/2.56	
5.53/2.56	----------------------------------------
5.53/2.56	
5.53/2.56	(0)
5.53/2.56	Obligation:
5.53/2.56	Complexity Int TRS consisting of the following rules:
5.53/2.56	eval_speedpldi2_start(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb0_in(v_m, v_n, v_v1_0, v_v2_0)) :|: TRUE
5.53/2.56	eval_speedpldi2_bb0_in(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_0(v_m, v_n, v_v1_0, v_v2_0)) :|: TRUE
5.53/2.56	eval_speedpldi2_0(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_1(v_m, v_n, v_v1_0, v_v2_0)) :|: TRUE
5.53/2.56	eval_speedpldi2_1(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_2(v_m, v_n, v_v1_0, v_v2_0)) :|: TRUE
5.53/2.56	eval_speedpldi2_2(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb1_in(v_m, v_n, v_n, 0)) :|: v_n >= 0 && v_m > 0
5.53/2.56	eval_speedpldi2_2(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb4_in(v_m, v_n, v_v1_0, v_v2_0)) :|: v_n < 0
5.53/2.56	eval_speedpldi2_2(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb4_in(v_m, v_n, v_v1_0, v_v2_0)) :|: v_m <= 0
5.53/2.56	eval_speedpldi2_bb1_in(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb2_in(v_m, v_n, v_v1_0, v_v2_0)) :|: v_v1_0 > 0
5.53/2.56	eval_speedpldi2_bb1_in(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb4_in(v_m, v_n, v_v1_0, v_v2_0)) :|: v_v1_0 <= 0
5.53/2.56	eval_speedpldi2_bb2_in(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb3_in(v_m, v_n, v_v1_0, v_v2_0)) :|: v_v2_0 < v_m
5.53/2.56	eval_speedpldi2_bb2_in(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb1_in(v_m, v_n, v_v1_0, 0)) :|: v_v2_0 >= v_m
5.53/2.56	eval_speedpldi2_bb3_in(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_bb1_in(v_m, v_n, v_v1_0 - 1, v_v2_0 + 1)) :|: TRUE
5.53/2.56	eval_speedpldi2_bb4_in(v_m, v_n, v_v1_0, v_v2_0) -> Com_1(eval_speedpldi2_stop(v_m, v_n, v_v1_0, v_v2_0)) :|: TRUE
5.53/2.56	
5.53/2.56	The start-symbols are:[eval_speedpldi2_start_4]
5.53/2.56	
5.53/2.56	
5.53/2.56	----------------------------------------
5.53/2.56	
5.53/2.56	(1) Koat Proof (FINISHED)
5.53/2.56	YES(?, 28*ar_0 + 15)
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Initial complexity problem:
5.53/2.56	
5.53/2.56	1:	T:
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\ ar_1 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1))
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.53/2.56	
5.53/2.56		start location:	koat_start
5.53/2.56	
5.53/2.56		leaf cost:	0
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.53/2.56	
5.53/2.56	2:	T:
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\ ar_1 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1))
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.53/2.56	
5.53/2.56		start location:	koat_start
5.53/2.56	
5.53/2.56		leaf cost:	0
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	A polynomial rank function with
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2start) = 2
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2bb0in) = 2
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi20) = 2
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi21) = 2
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi22) = 2
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2bb1in) = 2
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2bb4in) = 1
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2bb2in) = 2
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2bb3in) = 2
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2stop) = 0
5.53/2.56	
5.53/2.56		Pol(koat_start) = 2
5.53/2.56	
5.53/2.56	orients all transitions weakly and the transitions
5.53/2.56	
5.53/2.56		evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56		evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.53/2.56	
5.53/2.56	strictly and produces the following problem:
5.53/2.56	
5.53/2.56	3:	T:
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\ ar_1 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: 2, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1))
5.53/2.56	
5.53/2.56			(Comp: 2, Cost: 1)    evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.53/2.56	
5.53/2.56		start location:	koat_start
5.53/2.56	
5.53/2.56		leaf cost:	0
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Applied AI with 'oct' on problem 3 to obtain the following invariants:
5.53/2.56	
5.53/2.56	  For symbol evalspeedpldi2bb1in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
5.53/2.56	
5.53/2.56	  For symbol evalspeedpldi2bb2in: X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
5.53/2.56	
5.53/2.56	  For symbol evalspeedpldi2bb3in: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	This yielded the following problem:
5.53/2.56	
5.53/2.56	4:	T:
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.53/2.56	
5.53/2.56			(Comp: 2, Cost: 1)    evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: 2, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 ]
5.53/2.56	
5.53/2.56			(Comp: ?, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\ ar_1 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)    evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56		start location:	koat_start
5.53/2.56	
5.53/2.56		leaf cost:	0
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	A polynomial rank function with
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2bb3in) = 7*V_3 + 4*V_4 - 1
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2bb1in) = 7*V_3 + 4*V_4 + 1
5.53/2.56	
5.53/2.56		Pol(evalspeedpldi2bb2in) = 7*V_3 + 4*V_4
5.53/2.56	
5.53/2.56	and size complexities
5.53/2.56	
5.53/2.56		S("evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.53/2.56	
5.53/2.56		S("evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.53/2.56	
5.53/2.56		S("evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.53/2.56	
5.53/2.56		S("evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.53/2.56	
5.53/2.56		S("evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.53/2.56	
5.53/2.56		S("evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\\ ar_1 >= 1 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\\ ar_1 >= 1 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\\ ar_1 >= 1 ]", 0-2) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\\ ar_1 >= 1 ]", 0-3) = 0
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]", 0-2) = ar_2
5.53/2.56	
5.53/2.56		S("evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]", 0-3) = ar_3
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= 1 ]", 0-3) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_2 ]", 0-2) = 0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 ]", 0-2) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 ]", 0-3) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 ]", 0-2) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 ]", 0-3) = 0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.53/2.56	
5.53/2.56		S("evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_1 + ar_3
5.53/2.56	
5.53/2.56		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.53/2.56	
5.53/2.56		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.53/2.56	
5.53/2.56		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.53/2.56	
5.53/2.56		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.53/2.56	
5.53/2.56	orients the transitions
5.53/2.56	
5.53/2.56		evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
5.53/2.56	
5.53/2.56		evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.53/2.56	
5.53/2.56		evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 ]
5.53/2.56	
5.53/2.56		evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
5.53/2.56	
5.53/2.56	weakly and the transitions
5.53/2.56	
5.53/2.56		evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
5.53/2.56	
5.53/2.56		evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.53/2.56	
5.53/2.56		evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 ]
5.53/2.56	
5.53/2.56		evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
5.53/2.56	
5.53/2.56	strictly and produces the following problem:
5.53/2.56	
5.53/2.56	5:	T:
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.53/2.56	
5.53/2.56			(Comp: 2, Cost: 1)             evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2stop(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 7*ar_0 + 1, Cost: 1)    evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2 - 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ]
5.53/2.56	
5.53/2.56			(Comp: 7*ar_0 + 1, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: 7*ar_0 + 1, Cost: 1)    evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: 2, Cost: 1)             evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 ]
5.53/2.56	
5.53/2.56			(Comp: 7*ar_0 + 1, Cost: 1)    evalspeedpldi2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)             evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)             evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)             evalspeedpldi22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb1in(ar_0, ar_1, ar_0, 0)) [ ar_0 >= 0 /\ ar_1 >= 1 ]
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)             evalspeedpldi21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi22(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)             evalspeedpldi20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi21(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)             evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi20(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56			(Comp: 1, Cost: 1)             evalspeedpldi2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi2bb0in(ar_0, ar_1, ar_2, ar_3))
5.53/2.56	
5.53/2.56		start location:	koat_start
5.53/2.56	
5.53/2.56		leaf cost:	0
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Complexity upper bound 28*ar_0 + 15
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Time: 0.348 sec (SMT: 0.278 sec)
5.53/2.56	
5.53/2.56	
5.53/2.56	----------------------------------------
5.53/2.56	
5.53/2.56	(2)
5.53/2.56	BOUNDS(1, n^1)
5.53/2.56	
5.53/2.56	----------------------------------------
5.53/2.56	
5.53/2.56	(3) Loat Proof (FINISHED)
5.53/2.56	
5.53/2.56	
5.53/2.56	### Pre-processing the ITS problem ###
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Initial linear ITS problem
5.53/2.56	
5.53/2.56	   Start location: evalspeedpldi2start
5.53/2.56	
5.53/2.56	      0: evalspeedpldi2start -> evalspeedpldi2bb0in : [], cost: 1
5.53/2.56	
5.53/2.56	      1: evalspeedpldi2bb0in -> evalspeedpldi20 : [], cost: 1
5.53/2.56	
5.53/2.56	      2: evalspeedpldi20 -> evalspeedpldi21 : [], cost: 1
5.53/2.56	
5.53/2.56	      3: evalspeedpldi21 -> evalspeedpldi22 : [], cost: 1
5.53/2.56	
5.53/2.56	      4: evalspeedpldi22 -> evalspeedpldi2bb1in : C'=A, D'=0, [ A>=0 && B>=1 ], cost: 1
5.53/2.56	
5.53/2.56	      5: evalspeedpldi22 -> evalspeedpldi2bb4in : [ 0>=1+A ], cost: 1
5.53/2.56	
5.53/2.56	      6: evalspeedpldi22 -> evalspeedpldi2bb4in : [ 0>=B ], cost: 1
5.53/2.56	
5.53/2.56	      7: evalspeedpldi2bb1in -> evalspeedpldi2bb2in : [ C>=1 ], cost: 1
5.53/2.56	
5.53/2.56	      8: evalspeedpldi2bb1in -> evalspeedpldi2bb4in : [ 0>=C ], cost: 1
5.53/2.56	
5.53/2.56	      9: evalspeedpldi2bb2in -> evalspeedpldi2bb3in : [ B>=1+D ], cost: 1
5.53/2.56	
5.53/2.56	     10: evalspeedpldi2bb2in -> evalspeedpldi2bb1in : D'=0, [ D>=B ], cost: 1
5.53/2.56	
5.53/2.56	     11: evalspeedpldi2bb3in -> evalspeedpldi2bb1in : C'=-1+C, D'=1+D, [], cost: 1
5.53/2.56	
5.53/2.56	     12: evalspeedpldi2bb4in -> evalspeedpldi2stop : [], cost: 1
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Removed unreachable and leaf rules:
5.53/2.56	
5.53/2.56	   Start location: evalspeedpldi2start
5.53/2.56	
5.53/2.56	      0: evalspeedpldi2start -> evalspeedpldi2bb0in : [], cost: 1
5.53/2.56	
5.53/2.56	      1: evalspeedpldi2bb0in -> evalspeedpldi20 : [], cost: 1
5.53/2.56	
5.53/2.56	      2: evalspeedpldi20 -> evalspeedpldi21 : [], cost: 1
5.53/2.56	
5.53/2.56	      3: evalspeedpldi21 -> evalspeedpldi22 : [], cost: 1
5.53/2.56	
5.53/2.56	      4: evalspeedpldi22 -> evalspeedpldi2bb1in : C'=A, D'=0, [ A>=0 && B>=1 ], cost: 1
5.53/2.56	
5.53/2.56	      7: evalspeedpldi2bb1in -> evalspeedpldi2bb2in : [ C>=1 ], cost: 1
5.53/2.56	
5.53/2.56	      9: evalspeedpldi2bb2in -> evalspeedpldi2bb3in : [ B>=1+D ], cost: 1
5.53/2.56	
5.53/2.56	     10: evalspeedpldi2bb2in -> evalspeedpldi2bb1in : D'=0, [ D>=B ], cost: 1
5.53/2.56	
5.53/2.56	     11: evalspeedpldi2bb3in -> evalspeedpldi2bb1in : C'=-1+C, D'=1+D, [], cost: 1
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	### Simplification by acceleration and chaining ###
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Eliminated locations (on linear paths):
5.53/2.56	
5.53/2.56	   Start location: evalspeedpldi2start
5.53/2.56	
5.53/2.56	     16: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=A, D'=0, [ A>=0 && B>=1 ], cost: 5
5.53/2.56	
5.53/2.56	      7: evalspeedpldi2bb1in -> evalspeedpldi2bb2in : [ C>=1 ], cost: 1
5.53/2.56	
5.53/2.56	     10: evalspeedpldi2bb2in -> evalspeedpldi2bb1in : D'=0, [ D>=B ], cost: 1
5.53/2.56	
5.53/2.56	     17: evalspeedpldi2bb2in -> evalspeedpldi2bb1in : C'=-1+C, D'=1+D, [ B>=1+D ], cost: 2
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Eliminated locations (on tree-shaped paths):
5.53/2.56	
5.53/2.56	   Start location: evalspeedpldi2start
5.53/2.56	
5.53/2.56	     16: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=A, D'=0, [ A>=0 && B>=1 ], cost: 5
5.53/2.56	
5.53/2.56	     18: evalspeedpldi2bb1in -> evalspeedpldi2bb1in : D'=0, [ C>=1 && D>=B ], cost: 2
5.53/2.56	
5.53/2.56	     19: evalspeedpldi2bb1in -> evalspeedpldi2bb1in : C'=-1+C, D'=1+D, [ C>=1 && B>=1+D ], cost: 3
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Accelerating simple loops of location 5.
5.53/2.56	
5.53/2.56	   Accelerating the following rules:
5.53/2.56	
5.53/2.56	     18: evalspeedpldi2bb1in -> evalspeedpldi2bb1in : D'=0, [ C>=1 && D>=B ], cost: 2
5.53/2.56	
5.53/2.56	     19: evalspeedpldi2bb1in -> evalspeedpldi2bb1in : C'=-1+C, D'=1+D, [ C>=1 && B>=1+D ], cost: 3
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	   Accelerated rule 18 with NONTERM (after strengthening guard), yielding the new rule 20.
5.53/2.56	
5.53/2.56	   Accelerated rule 19 with backward acceleration, yielding the new rule 21.
5.53/2.56	
5.53/2.56	   Accelerated rule 19 with backward acceleration, yielding the new rule 22.
5.53/2.56	
5.53/2.56	   Removing the simple loops: 19.
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Accelerated all simple loops using metering functions (where possible):
5.53/2.56	
5.53/2.56	   Start location: evalspeedpldi2start
5.53/2.56	
5.53/2.56	     16: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=A, D'=0, [ A>=0 && B>=1 ], cost: 5
5.53/2.56	
5.53/2.56	     18: evalspeedpldi2bb1in -> evalspeedpldi2bb1in : D'=0, [ C>=1 && D>=B ], cost: 2
5.53/2.56	
5.53/2.56	     20: evalspeedpldi2bb1in -> [10] : [ C>=1 && D>=B && 0>=B ], cost: INF
5.53/2.56	
5.53/2.56	     21: evalspeedpldi2bb1in -> evalspeedpldi2bb1in : C'=0, D'=C+D, [ C>=1 && B>=1+D && B>=C+D ], cost: 3*C
5.53/2.56	
5.53/2.56	     22: evalspeedpldi2bb1in -> evalspeedpldi2bb1in : C'=C+D-B, D'=B, [ C>=1 && B>=1+D && 1+C+D-B>=1 ], cost: -3*D+3*B
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Chained accelerated rules (with incoming rules):
5.53/2.56	
5.53/2.56	   Start location: evalspeedpldi2start
5.53/2.56	
5.53/2.56	     16: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=A, D'=0, [ A>=0 && B>=1 ], cost: 5
5.53/2.56	
5.53/2.56	     23: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=0, D'=A, [ B>=1 && A>=1 && B>=A ], cost: 5+3*A
5.53/2.56	
5.53/2.56	     24: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=A-B, D'=B, [ B>=1 && A>=1 && 1+A-B>=1 ], cost: 5+3*B
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Removed unreachable locations (and leaf rules with constant cost):
5.53/2.56	
5.53/2.56	   Start location: evalspeedpldi2start
5.53/2.56	
5.53/2.56	     23: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=0, D'=A, [ B>=1 && A>=1 && B>=A ], cost: 5+3*A
5.53/2.56	
5.53/2.56	     24: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=A-B, D'=B, [ B>=1 && A>=1 && 1+A-B>=1 ], cost: 5+3*B
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	### Computing asymptotic complexity ###
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Fully simplified ITS problem
5.53/2.56	
5.53/2.56	   Start location: evalspeedpldi2start
5.53/2.56	
5.53/2.56	     23: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=0, D'=A, [ B>=1 && A>=1 && B>=A ], cost: 5+3*A
5.53/2.56	
5.53/2.56	     24: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=A-B, D'=B, [ B>=1 && A>=1 && 1+A-B>=1 ], cost: 5+3*B
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Computing asymptotic complexity for rule 23
5.53/2.56	
5.53/2.56	   Simplified the guard:
5.53/2.56	
5.53/2.56	     23: evalspeedpldi2start -> evalspeedpldi2bb1in : C'=0, D'=A, [ A>=1 && B>=A ], cost: 5+3*A
5.53/2.56	
5.53/2.56	   Solved the limit problem by the following transformations:
5.53/2.56	
5.53/2.56	      Created initial limit problem:
5.53/2.56	
5.53/2.56	      5+3*A (+), A (+/+!), 1-A+B (+/+!) [not solved]
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	      removing all constraints (solved by SMT)
5.53/2.56	
5.53/2.56	      resulting limit problem: [solved]
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	      applying transformation rule (C) using substitution {A==n,B==2*n}
5.53/2.56	
5.53/2.56	      resulting limit problem:
5.53/2.56	
5.53/2.56	      [solved]
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	   Solution:
5.53/2.56	
5.53/2.56	      A / n
5.53/2.56	
5.53/2.56	      B / 2*n
5.53/2.56	
5.53/2.56	   Resulting cost 5+3*n has complexity: Poly(n^1)
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Found new complexity Poly(n^1).
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	Obtained the following overall complexity (w.r.t. the length of the input n):
5.53/2.56	
5.53/2.56	   Complexity:  Poly(n^1)
5.53/2.56	
5.53/2.56	   Cpx degree:  1
5.53/2.56	
5.53/2.56	   Solved cost: 5+3*n
5.53/2.56	
5.53/2.56	   Rule cost:   5+3*A
5.53/2.56	
5.53/2.56	   Rule guard:  [ A>=1 && B>=A ]
5.53/2.56	
5.53/2.56	
5.53/2.56	
5.53/2.56	WORST_CASE(Omega(n^1),?)
5.53/2.56	
5.53/2.56	
5.53/2.56	----------------------------------------
5.53/2.56	
5.53/2.56	(4)
5.53/2.56	BOUNDS(n^1, INF)
5.67/2.60	EOF