2.11/1.30	WORST_CASE(?, O(n^1))
2.11/1.31	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.11/1.31	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.11/1.31	
2.11/1.31	
2.11/1.31	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.11/1.31	
2.11/1.31	(0) CpxIntTrs
2.11/1.31	(1) Koat Proof [FINISHED, 75 ms]
2.11/1.31	(2) BOUNDS(1, n^1)
2.11/1.31	
2.11/1.31	
2.11/1.31	----------------------------------------
2.11/1.31	
2.11/1.31	(0)
2.11/1.31	Obligation:
2.11/1.31	Complexity Int TRS consisting of the following rules:
2.11/1.31	eval_t20_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.11/1.31	eval_t20_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb1_in(v_x, v_.01, v_x, v_y)) :|: TRUE
2.11/1.31	eval_t20_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < v_y
2.11/1.31	eval_t20_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb3_in(v_.0, v_y, v_x, v_y)) :|: v_.0 >= v_y
2.11/1.31	eval_t20_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb1_in(v_.0 + 1, v_.01, v_x, v_y)) :|: TRUE
2.11/1.31	eval_t20_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb4_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 < v_.0
2.11/1.31	eval_t20_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb5_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 >= v_.0
2.11/1.31	eval_t20_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb3_in(v_.0, v_.01 + 1, v_x, v_y)) :|: TRUE
2.11/1.31	eval_t20_bb5_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.11/1.31	
2.11/1.31	The start-symbols are:[eval_t20_start_4]
2.11/1.31	
2.11/1.31	
2.11/1.31	----------------------------------------
2.11/1.31	
2.11/1.31	(1) Koat Proof (FINISHED)
2.11/1.31	YES(?, 14*ar_1 + 20*ar_2 + 17)
2.11/1.31	
2.11/1.31	
2.11/1.31	
2.11/1.31	Initial complexity problem:
2.11/1.31	
2.11/1.31	1:	T:
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))
2.11/1.31	
2.11/1.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.11/1.31	
2.11/1.31		start location:	koat_start
2.11/1.31	
2.11/1.31		leaf cost:	0
2.11/1.31	
2.11/1.31	
2.11/1.31	
2.11/1.31	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.11/1.31	
2.11/1.31	2:	T:
2.11/1.31	
2.11/1.31			(Comp: 1, Cost: 1)    evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))
2.11/1.31	
2.11/1.31			(Comp: 1, Cost: 1)    evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))
2.11/1.31	
2.11/1.31			(Comp: ?, Cost: 1)    evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))
2.11/1.31	
2.11/1.31			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.11/1.31	
2.11/1.31		start location:	koat_start
2.11/1.31	
2.11/1.31		leaf cost:	0
2.11/1.31	
2.11/1.31	
2.11/1.31	
2.11/1.31	A polynomial rank function with
2.11/1.31	
2.11/1.31		Pol(evalt20start) = 3
2.11/1.32	
2.11/1.32		Pol(evalt20bb0in) = 3
2.11/1.32	
2.11/1.32		Pol(evalt20bb1in) = 3
2.11/1.32	
2.11/1.32		Pol(evalt20bb2in) = 3
2.11/1.32	
2.11/1.32		Pol(evalt20bb3in) = 2
2.11/1.32	
2.11/1.32		Pol(evalt20bb4in) = 2
2.11/1.32	
2.11/1.32		Pol(evalt20bb5in) = 1
2.11/1.32	
2.11/1.32		Pol(evalt20stop) = 0
2.11/1.32	
2.11/1.32		Pol(koat_start) = 3
2.11/1.32	
2.11/1.32	orients all transitions weakly and the transitions
2.11/1.32	
2.11/1.32		evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32		evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]
2.11/1.32	
2.11/1.32		evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]
2.11/1.32	
2.11/1.32	strictly and produces the following problem:
2.11/1.32	
2.11/1.32	3:	T:
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)    evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)    evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)    evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)    evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)    evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)    evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)    evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)    evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)    evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.11/1.32	
2.11/1.32		start location:	koat_start
2.11/1.32	
2.11/1.32		leaf cost:	0
2.11/1.32	
2.11/1.32	
2.11/1.32	
2.11/1.32	A polynomial rank function with
2.11/1.32	
2.11/1.32		Pol(evalt20start) = -V_2 + V_3
2.11/1.32	
2.11/1.32		Pol(evalt20bb0in) = -V_2 + V_3
2.11/1.32	
2.11/1.32		Pol(evalt20bb1in) = -V_1 + V_3
2.11/1.32	
2.11/1.32		Pol(evalt20bb2in) = -V_1 + V_3 - 1
2.11/1.32	
2.11/1.32		Pol(evalt20bb3in) = -V_1 + V_3
2.11/1.32	
2.11/1.32		Pol(evalt20bb4in) = -V_1 + V_3
2.11/1.32	
2.11/1.32		Pol(evalt20bb5in) = -V_1 + V_3
2.11/1.32	
2.11/1.32		Pol(evalt20stop) = -V_1 + V_3
2.11/1.32	
2.11/1.32		Pol(koat_start) = -V_2 + V_3
2.11/1.32	
2.11/1.32	orients all transitions weakly and the transition
2.11/1.32	
2.11/1.32		evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.11/1.32	
2.11/1.32	strictly and produces the following problem:
2.11/1.32	
2.11/1.32	4:	T:
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)              evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)              evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: ar_1 + ar_2, Cost: 1)    evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)              evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)              evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)              evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)              evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)              evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)              evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.11/1.32	
2.11/1.32		start location:	koat_start
2.11/1.32	
2.11/1.32		leaf cost:	0
2.11/1.32	
2.11/1.32	
2.11/1.32	
2.11/1.32	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.11/1.32	
2.11/1.32	5:	T:
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)              evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)              evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: ar_1 + ar_2, Cost: 1)    evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)              evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]
2.11/1.32	
2.11/1.32			(Comp: ar_1 + ar_2, Cost: 1)    evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)              evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)              evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)              evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)              evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.11/1.32	
2.11/1.32		start location:	koat_start
2.11/1.32	
2.11/1.32		leaf cost:	0
2.11/1.32	
2.11/1.32	
2.11/1.32	
2.11/1.32	A polynomial rank function with
2.11/1.32	
2.11/1.32		Pol(evalt20bb4in) = V_1 - V_4
2.11/1.32	
2.11/1.32		Pol(evalt20bb3in) = V_1 - V_4 + 1
2.11/1.32	
2.11/1.32	and size complexities
2.11/1.32	
2.11/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.11/1.32	
2.11/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.11/1.32	
2.11/1.32		S("evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 2*ar_1 + 2*ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.11/1.32	
2.11/1.32		S("evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))", 0-0) = 2*ar_1 + 2*ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))", 0-3) = ?
2.11/1.32	
2.11/1.32		S("evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]", 0-0) = 2*ar_1 + 2*ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]", 0-3) = ?
2.11/1.32	
2.11/1.32		S("evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 2*ar_1 + 2*ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ?
2.11/1.32	
2.11/1.32		S("evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-0) = 2*ar_1 + 2*ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.11/1.32	
2.11/1.32		S("evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]", 0-0) = 2*ar_1 + 2*ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]", 0-3) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-0) = 2*ar_1 + 2*ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
2.11/1.32	
2.11/1.32		S("evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.11/1.32	
2.11/1.32		S("evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.11/1.32	
2.11/1.32		S("evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.11/1.32	
2.11/1.32		S("evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.11/1.32	
2.11/1.32		S("evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.11/1.32	
2.11/1.32	orients the transitions
2.11/1.32	
2.11/1.32		evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))
2.11/1.32	
2.11/1.32		evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.32	
2.11/1.32	weakly and the transition
2.11/1.32	
2.11/1.32		evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.32	
2.11/1.32	strictly and produces the following problem:
2.11/1.32	
2.11/1.32	6:	T:
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)                      evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)                      evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: ar_1 + ar_2, Cost: 1)            evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)                      evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]
2.11/1.32	
2.11/1.32			(Comp: ar_1 + ar_2, Cost: 1)            evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 6*ar_1 + 9*ar_2 + 3, Cost: 1)    evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)                      evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]
2.11/1.32	
2.11/1.32			(Comp: ?, Cost: 1)                      evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)                      evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.11/1.32	
2.11/1.32		start location:	koat_start
2.11/1.32	
2.11/1.32		leaf cost:	0
2.11/1.32	
2.11/1.32	
2.11/1.32	
2.11/1.32	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.11/1.32	
2.11/1.32	7:	T:
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)                      evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 1)                      evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: ar_1 + ar_2, Cost: 1)            evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)                      evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ]
2.11/1.32	
2.11/1.32			(Comp: ar_1 + ar_2, Cost: 1)            evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 6*ar_1 + 9*ar_2 + 3, Cost: 1)    evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ]
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)                      evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ]
2.11/1.32	
2.11/1.32			(Comp: 6*ar_1 + 9*ar_2 + 3, Cost: 1)    evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1))
2.11/1.32	
2.11/1.32			(Comp: 3, Cost: 1)                      evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3))
2.11/1.32	
2.11/1.32			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.11/1.32	
2.11/1.32		start location:	koat_start
2.11/1.32	
2.11/1.32		leaf cost:	0
2.11/1.32	
2.11/1.32	
2.11/1.32	
2.11/1.32	Complexity upper bound 14*ar_1 + 20*ar_2 + 17
2.11/1.32	
2.11/1.32	
2.11/1.32	
2.11/1.32	Time: 0.101 sec (SMT: 0.086 sec)
2.11/1.32	
2.11/1.32	
2.11/1.32	----------------------------------------
2.11/1.32	
2.11/1.32	(2)
2.11/1.32	BOUNDS(1, n^1)
2.11/1.34	EOF