2.13/1.30	WORST_CASE(?, O(n^1))
2.13/1.31	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.13/1.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.13/1.31	
2.13/1.31	
2.13/1.31	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.13/1.31	
2.13/1.31	(0) CpxIntTrs
2.13/1.31	(1) Koat Proof [FINISHED, 75 ms]
2.13/1.31	(2) BOUNDS(1, n^1)
2.13/1.31	
2.13/1.31	
2.13/1.31	----------------------------------------
2.13/1.31	
2.13/1.31	(0)
2.13/1.31	Obligation:
2.13/1.31	Complexity Int TRS consisting of the following rules:
2.13/1.31	eval_speed_pldi10_ex4_start(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb0_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n)) :|: TRUE
2.13/1.31	eval_speed_pldi10_ex4_bb0_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb1_in(v_n, v_.1, 1, v_flag.1, v_n)) :|: TRUE
2.13/1.31	eval_speed_pldi10_ex4_bb1_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb2_in(v_.0, v_.0, v_flag.0, 0, v_n)) :|: v_flag.0 > 0
2.13/1.31	eval_speed_pldi10_ex4_bb1_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb4_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n)) :|: v_flag.0 <= 0
2.13/1.31	eval_speed_pldi10_ex4_bb2_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb3_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n)) :|: v_.1 > 0
2.13/1.31	eval_speed_pldi10_ex4_bb2_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb1_in(v_.1, v_.1, v_flag.1, v_flag.1, v_n)) :|: v_.1 <= 0
2.13/1.31	eval_speed_pldi10_ex4_bb3_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb2_in(v_.0, v_.1 - 1, v_flag.0, 1, v_n)) :|: TRUE
2.13/1.31	eval_speed_pldi10_ex4_bb4_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_stop(v_.0, v_.1, v_flag.0, v_flag.1, v_n)) :|: TRUE
2.13/1.31	
2.13/1.31	The start-symbols are:[eval_speed_pldi10_ex4_start_5]
2.13/1.31	
2.13/1.31	
2.13/1.31	----------------------------------------
2.13/1.31	
2.13/1.31	(1) Koat Proof (FINISHED)
2.13/1.31	YES(?, 5*ar_1 + 8)
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	Initial complexity problem:
2.13/1.31	
2.13/1.31	1:	T:
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.13/1.31	
2.13/1.31		start location:	koat_start
2.13/1.31	
2.13/1.31		leaf cost:	0
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.13/1.31	
2.13/1.31	2:	T:
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)    evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)    evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.13/1.31	
2.13/1.31		start location:	koat_start
2.13/1.31	
2.13/1.31		leaf cost:	0
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	A polynomial rank function with
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4start) = 2
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb0in) = 2
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb1in) = 2
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb2in) = 2
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb4in) = 1
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb3in) = 2
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4stop) = 0
2.13/1.31	
2.13/1.31		Pol(koat_start) = 2
2.13/1.31	
2.13/1.31	orients all transitions weakly and the transitions
2.13/1.31	
2.13/1.31		evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31		evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.13/1.31	
2.13/1.31	strictly and produces the following problem:
2.13/1.31	
2.13/1.31	3:	T:
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)    evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)    evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)    evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)    evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)    evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.13/1.31	
2.13/1.31		start location:	koat_start
2.13/1.31	
2.13/1.31		leaf cost:	0
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	A polynomial rank function with
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4start) = V_2
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb0in) = V_2
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb1in) = V_1
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb2in) = V_4
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb4in) = V_1
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb3in) = V_4 - 1
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4stop) = V_1
2.13/1.31	
2.13/1.31		Pol(koat_start) = V_2
2.13/1.31	
2.13/1.31	orients all transitions weakly and the transition
2.13/1.31	
2.13/1.31		evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
2.13/1.31	
2.13/1.31	strictly and produces the following problem:
2.13/1.31	
2.13/1.31	4:	T:
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)       evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)       evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)       evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)       evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.13/1.31	
2.13/1.31			(Comp: ar_1, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)       evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)       evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)       evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.13/1.31	
2.13/1.31		start location:	koat_start
2.13/1.31	
2.13/1.31		leaf cost:	0
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.13/1.31	
2.13/1.31	5:	T:
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)       evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)       evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)       evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)       evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.13/1.31	
2.13/1.31			(Comp: ar_1, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)       evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
2.13/1.31	
2.13/1.31			(Comp: ar_1, Cost: 1)    evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)       evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.13/1.31	
2.13/1.31		start location:	koat_start
2.13/1.31	
2.13/1.31		leaf cost:	0
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	A polynomial rank function with
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb2in) = V_5
2.13/1.31	
2.13/1.31		Pol(evalspeedpldi10ex4bb1in) = V_3
2.13/1.31	
2.13/1.31	and size complexities
2.13/1.31	
2.13/1.31		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
2.13/1.31	
2.13/1.31		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
2.13/1.31	
2.13/1.31		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
2.13/1.31	
2.13/1.31		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-0) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-2) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-3) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-4) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-0) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-2) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-3) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-4) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-0) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-2) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-3) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-4) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-0) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-2) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-3) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-4) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-0) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-2) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-3) = 2*ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-4) = 0
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-0) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-2) = 1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-3) = ar_3
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-4) = ar_4
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
2.13/1.31	
2.13/1.31		S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
2.13/1.31	
2.13/1.31	orients the transitions
2.13/1.31	
2.13/1.31		evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
2.13/1.31	
2.13/1.31		evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31	weakly and the transition
2.13/1.31	
2.13/1.31		evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31	strictly and produces the following problem:
2.13/1.31	
2.13/1.31	6:	T:
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)           evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)           evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: ar_1 + 1, Cost: 1)    evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)           evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.13/1.31	
2.13/1.31			(Comp: ar_1, Cost: 1)        evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: ?, Cost: 1)           evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
2.13/1.31	
2.13/1.31			(Comp: ar_1, Cost: 1)        evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)           evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.13/1.31	
2.13/1.31		start location:	koat_start
2.13/1.31	
2.13/1.31		leaf cost:	0
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.13/1.31	
2.13/1.31	7:	T:
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)             evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 1)             evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: ar_1 + 1, Cost: 1)      evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)             evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]
2.13/1.31	
2.13/1.31			(Comp: ar_1, Cost: 1)          evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]
2.13/1.31	
2.13/1.31			(Comp: 2*ar_1 + 1, Cost: 1)    evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]
2.13/1.31	
2.13/1.31			(Comp: ar_1, Cost: 1)          evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))
2.13/1.31	
2.13/1.31			(Comp: 2, Cost: 1)             evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))
2.13/1.31	
2.13/1.31			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
2.13/1.31	
2.13/1.31		start location:	koat_start
2.13/1.31	
2.13/1.31		leaf cost:	0
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	Complexity upper bound 5*ar_1 + 8
2.13/1.31	
2.13/1.31	
2.13/1.31	
2.13/1.31	Time: 0.097 sec (SMT: 0.082 sec)
2.13/1.31	
2.13/1.31	
2.13/1.31	----------------------------------------
2.13/1.31	
2.13/1.31	(2)
2.13/1.31	BOUNDS(1, n^1)
2.13/1.34	EOF