2.22/1.32	WORST_CASE(?, O(n^1))
2.35/1.33	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.35/1.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.35/1.33	
2.35/1.33	
2.35/1.33	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.35/1.33	
2.35/1.33	(0) CpxIntTrs
2.35/1.33	(1) Koat Proof [FINISHED, 85 ms]
2.35/1.33	(2) BOUNDS(1, n^1)
2.35/1.33	
2.35/1.33	
2.35/1.33	----------------------------------------
2.35/1.33	
2.35/1.33	(0)
2.35/1.33	Obligation:
2.35/1.33	Complexity Int TRS consisting of the following rules:
2.35/1.33	eval_t08_start(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb0_in(v_.0, v_.1, v_y, v_z)) :|: TRUE
2.35/1.33	eval_t08_bb0_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb1_in(v_y, v_.1, v_y, v_z)) :|: TRUE
2.35/1.33	eval_t08_bb1_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb2_in(v_.0, v_.1, v_y, v_z)) :|: v_z > v_.0
2.35/1.33	eval_t08_bb1_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb3_in(v_.0, v_.0, v_y, v_z)) :|: v_z <= v_.0
2.35/1.33	eval_t08_bb2_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb1_in(v_.0 + 1, v_.1, v_y, v_z)) :|: TRUE
2.35/1.33	eval_t08_bb3_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb4_in(v_.0, v_.1, v_y, v_z)) :|: v_.1 > 2
2.35/1.33	eval_t08_bb3_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb5_in(v_.0, v_.1, v_y, v_z)) :|: v_.1 <= 2
2.35/1.33	eval_t08_bb4_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb3_in(v_.0, v_.1 - 3, v_y, v_z)) :|: TRUE
2.35/1.33	eval_t08_bb5_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_stop(v_.0, v_.1, v_y, v_z)) :|: TRUE
2.35/1.33	
2.35/1.33	The start-symbols are:[eval_t08_start_4]
2.35/1.33	
2.35/1.33	
2.35/1.33	----------------------------------------
2.35/1.33	
2.35/1.33	(1) Koat Proof (FINISHED)
2.35/1.33	YES(?, 14*ar_1 + 14*ar_2 + 11)
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	Initial complexity problem:
2.35/1.33	
2.35/1.33	1:	T:
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.35/1.33	
2.35/1.33		start location:	koat_start
2.35/1.33	
2.35/1.33		leaf cost:	0
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.35/1.33	
2.35/1.33	2:	T:
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)    evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)    evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.35/1.33	
2.35/1.33		start location:	koat_start
2.35/1.33	
2.35/1.33		leaf cost:	0
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	A polynomial rank function with
2.35/1.33	
2.35/1.33		Pol(evalt08start) = 3
2.35/1.33	
2.35/1.33		Pol(evalt08bb0in) = 3
2.35/1.33	
2.35/1.33		Pol(evalt08bb1in) = 3
2.35/1.33	
2.35/1.33		Pol(evalt08bb2in) = 3
2.35/1.33	
2.35/1.33		Pol(evalt08bb3in) = 2
2.35/1.33	
2.35/1.33		Pol(evalt08bb4in) = 2
2.35/1.33	
2.35/1.33		Pol(evalt08bb5in) = 1
2.35/1.33	
2.35/1.33		Pol(evalt08stop) = 0
2.35/1.33	
2.35/1.33		Pol(koat_start) = 3
2.35/1.33	
2.35/1.33	orients all transitions weakly and the transitions
2.35/1.33	
2.35/1.33		evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33		evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
2.35/1.33	
2.35/1.33		evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]
2.35/1.33	
2.35/1.33	strictly and produces the following problem:
2.35/1.33	
2.35/1.33	3:	T:
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)    evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)    evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)    evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)    evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)    evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)    evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.35/1.33	
2.35/1.33		start location:	koat_start
2.35/1.33	
2.35/1.33		leaf cost:	0
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	A polynomial rank function with
2.35/1.33	
2.35/1.33		Pol(evalt08start) = -V_2 + V_3
2.35/1.33	
2.35/1.33		Pol(evalt08bb0in) = -V_2 + V_3
2.35/1.33	
2.35/1.33		Pol(evalt08bb1in) = -V_1 + V_3
2.35/1.33	
2.35/1.33		Pol(evalt08bb2in) = -V_1 + V_3 - 1
2.35/1.33	
2.35/1.33		Pol(evalt08bb3in) = -V_1 + V_3
2.35/1.33	
2.35/1.33		Pol(evalt08bb4in) = -V_1 + V_3
2.35/1.33	
2.35/1.33		Pol(evalt08bb5in) = -V_1 + V_3
2.35/1.33	
2.35/1.33		Pol(evalt08stop) = -V_1 + V_3
2.35/1.33	
2.35/1.33		Pol(koat_start) = -V_2 + V_3
2.35/1.33	
2.35/1.33	orients all transitions weakly and the transition
2.35/1.33	
2.35/1.33		evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.35/1.33	
2.35/1.33	strictly and produces the following problem:
2.35/1.33	
2.35/1.33	4:	T:
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)              evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)              evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ar_1 + ar_2, Cost: 1)    evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)              evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)              evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)              evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)              evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)              evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)              evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.35/1.33	
2.35/1.33		start location:	koat_start
2.35/1.33	
2.35/1.33		leaf cost:	0
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.35/1.33	
2.35/1.33	5:	T:
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)              evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)              evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ar_1 + ar_2, Cost: 1)    evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)              evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]
2.35/1.33	
2.35/1.33			(Comp: ar_1 + ar_2, Cost: 1)    evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)              evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)              evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)              evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)              evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.35/1.33	
2.35/1.33		start location:	koat_start
2.35/1.33	
2.35/1.33		leaf cost:	0
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	A polynomial rank function with
2.35/1.33	
2.35/1.33		Pol(evalt08bb4in) = V_4 - 3
2.35/1.33	
2.35/1.33		Pol(evalt08bb3in) = V_4
2.35/1.33	
2.35/1.33	and size complexities
2.35/1.33	
2.35/1.33		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.35/1.33	
2.35/1.33		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.35/1.33	
2.35/1.33		S("evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 2*ar_1 + 2*ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.35/1.33	
2.35/1.33		S("evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))", 0-0) = 2*ar_1 + 2*ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))", 0-3) = ?
2.35/1.33	
2.35/1.33		S("evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]", 0-0) = 2*ar_1 + 2*ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]", 0-3) = ?
2.35/1.33	
2.35/1.33		S("evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]", 0-0) = 2*ar_1 + 2*ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]", 0-3) = ?
2.35/1.33	
2.35/1.33		S("evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-0) = 2*ar_1 + 2*ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.35/1.33	
2.35/1.33		S("evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]", 0-0) = 2*ar_1 + 2*ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]", 0-3) = 2*ar_1 + 2*ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-0) = 2*ar_1 + 2*ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
2.35/1.33	
2.35/1.33		S("evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.35/1.33	
2.35/1.33		S("evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.35/1.33	
2.35/1.33		S("evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.35/1.33	
2.35/1.33		S("evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.35/1.33	
2.35/1.33		S("evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.35/1.33	
2.35/1.33	orients the transitions
2.35/1.33	
2.35/1.33		evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))
2.35/1.33	
2.35/1.33		evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33	weakly and the transition
2.35/1.33	
2.35/1.33		evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33	strictly and produces the following problem:
2.35/1.33	
2.35/1.33	6:	T:
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)                  evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)                  evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ar_1 + ar_2, Cost: 1)        evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)                  evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]
2.35/1.33	
2.35/1.33			(Comp: ar_1 + ar_2, Cost: 1)        evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 6*ar_1 + 6*ar_2, Cost: 1)    evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)                  evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
2.35/1.33	
2.35/1.33			(Comp: ?, Cost: 1)                  evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)                  evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.35/1.33	
2.35/1.33		start location:	koat_start
2.35/1.33	
2.35/1.33		leaf cost:	0
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.35/1.33	
2.35/1.33	7:	T:
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)                  evalt08start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb0in(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 1)                  evalt08bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: ar_1 + ar_2, Cost: 1)        evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)                  evalt08bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_0 >= ar_2 ]
2.35/1.33	
2.35/1.33			(Comp: ar_1 + ar_2, Cost: 1)        evalt08bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 6*ar_1 + 6*ar_2, Cost: 1)    evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 3 ]
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)                  evalt08bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_3 ]
2.35/1.33	
2.35/1.33			(Comp: 6*ar_1 + 6*ar_2, Cost: 1)    evalt08bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08bb3in(ar_0, ar_1, ar_2, ar_3 - 3))
2.35/1.33	
2.35/1.33			(Comp: 3, Cost: 1)                  evalt08bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08stop(ar_0, ar_1, ar_2, ar_3))
2.35/1.33	
2.35/1.33			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt08start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.35/1.33	
2.35/1.33		start location:	koat_start
2.35/1.33	
2.35/1.33		leaf cost:	0
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	Complexity upper bound 14*ar_1 + 14*ar_2 + 11
2.35/1.33	
2.35/1.33	
2.35/1.33	
2.35/1.33	Time: 0.100 sec (SMT: 0.086 sec)
2.35/1.33	
2.35/1.33	
2.35/1.33	----------------------------------------
2.35/1.33	
2.35/1.33	(2)
2.35/1.33	BOUNDS(1, n^1)
2.35/1.35	EOF