2.31/1.42	WORST_CASE(?, O(n^1))
2.31/1.43	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.31/1.43	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.31/1.43	
2.31/1.43	
2.31/1.43	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.31/1.43	
2.31/1.43	(0) CpxIntTrs
2.31/1.43	(1) Koat Proof [FINISHED, 187 ms]
2.31/1.43	(2) BOUNDS(1, n^1)
2.31/1.43	
2.31/1.43	
2.31/1.43	----------------------------------------
2.31/1.43	
2.31/1.43	(0)
2.31/1.43	Obligation:
2.31/1.43	Complexity Int TRS consisting of the following rules:
2.31/1.43	eval_t19_start(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb0_in(v_.0, v_.1, v_i, v_k)) :|: TRUE
2.31/1.43	eval_t19_bb0_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb1_in(v_i, v_.1, v_i, v_k)) :|: TRUE
2.31/1.43	eval_t19_bb1_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb2_in(v_.0, v_.1, v_i, v_k)) :|: v_.0 > 100
2.31/1.43	eval_t19_bb1_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb3_in(v_.0, v_.1, v_i, v_k)) :|: v_.0 <= 100
2.31/1.43	eval_t19_bb2_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb1_in(v_.0 - 1, v_.1, v_i, v_k)) :|: TRUE
2.31/1.43	eval_t19_bb3_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb4_in(v_.0, v_.0 + v_k + 50, v_i, v_k)) :|: TRUE
2.31/1.43	eval_t19_bb4_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb5_in(v_.0, v_.1, v_i, v_k)) :|: v_.1 >= 0
2.31/1.43	eval_t19_bb4_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb6_in(v_.0, v_.1, v_i, v_k)) :|: v_.1 < 0
2.31/1.43	eval_t19_bb5_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb4_in(v_.0, v_.1 - 1, v_i, v_k)) :|: TRUE
2.31/1.43	eval_t19_bb6_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_stop(v_.0, v_.1, v_i, v_k)) :|: TRUE
2.31/1.43	
2.31/1.43	The start-symbols are:[eval_t19_start_4]
2.31/1.43	
2.31/1.43	
2.31/1.43	----------------------------------------
2.31/1.43	
2.31/1.43	(1) Koat Proof (FINISHED)
2.31/1.43	YES(?, 2*ar_1 + 2*ar_3 + 422)
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	Initial complexity problem:
2.31/1.43	
2.31/1.43	1:	T:
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.31/1.43	
2.31/1.43		start location:	koat_start
2.31/1.43	
2.31/1.43		leaf cost:	0
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.31/1.43	
2.31/1.43	2:	T:
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)    evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)    evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.31/1.43	
2.31/1.43		start location:	koat_start
2.31/1.43	
2.31/1.43		leaf cost:	0
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	A polynomial rank function with
2.31/1.43	
2.31/1.43		Pol(evalt19start) = 4
2.31/1.43	
2.31/1.43		Pol(evalt19bb0in) = 4
2.31/1.43	
2.31/1.43		Pol(evalt19bb1in) = 4
2.31/1.43	
2.31/1.43		Pol(evalt19bb2in) = 4
2.31/1.43	
2.31/1.43		Pol(evalt19bb3in) = 3
2.31/1.43	
2.31/1.43		Pol(evalt19bb4in) = 2
2.31/1.43	
2.31/1.43		Pol(evalt19bb5in) = 2
2.31/1.43	
2.31/1.43		Pol(evalt19bb6in) = 1
2.31/1.43	
2.31/1.43		Pol(evalt19stop) = 0
2.31/1.43	
2.31/1.43		Pol(koat_start) = 4
2.31/1.43	
2.31/1.43	orients all transitions weakly and the transitions
2.31/1.43	
2.31/1.43		evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43		evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.31/1.43	
2.31/1.43		evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3))
2.31/1.43	
2.31/1.43		evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
2.31/1.43	
2.31/1.43	strictly and produces the following problem:
2.31/1.43	
2.31/1.43	3:	T:
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)    evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)    evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)    evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)    evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)    evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)    evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)    evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.31/1.43	
2.31/1.43		start location:	koat_start
2.31/1.43	
2.31/1.43		leaf cost:	0
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	A polynomial rank function with
2.31/1.43	
2.31/1.43		Pol(evalt19start) = V_2 + 51
2.31/1.43	
2.31/1.43		Pol(evalt19bb0in) = V_2 + 51
2.31/1.43	
2.31/1.43		Pol(evalt19bb1in) = V_1 + 51
2.31/1.43	
2.31/1.43		Pol(evalt19bb2in) = V_1 + 50
2.31/1.43	
2.31/1.43		Pol(evalt19bb3in) = V_1 + 51
2.31/1.43	
2.31/1.43		Pol(evalt19bb4in) = V_3 - V_4 + 1
2.31/1.43	
2.31/1.43		Pol(evalt19bb5in) = V_3 - V_4
2.31/1.43	
2.31/1.43		Pol(evalt19bb6in) = V_3 - V_4
2.31/1.43	
2.31/1.43		Pol(evalt19stop) = V_3 - V_4
2.31/1.43	
2.31/1.43		Pol(koat_start) = V_2 + 51
2.31/1.43	
2.31/1.43	orients all transitions weakly and the transition
2.31/1.43	
2.31/1.43		evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
2.31/1.43	
2.31/1.43	strictly and produces the following problem:
2.31/1.43	
2.31/1.43	4:	T:
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)            evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)            evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ar_1 + 51, Cost: 1)    evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)            evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)            evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)            evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)            evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)            evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)            evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)            evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 0)            koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.31/1.43	
2.31/1.43		start location:	koat_start
2.31/1.43	
2.31/1.43		leaf cost:	0
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.31/1.43	
2.31/1.43	5:	T:
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)            evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)            evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ar_1 + 51, Cost: 1)    evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)            evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
2.31/1.43	
2.31/1.43			(Comp: ar_1 + 51, Cost: 1)    evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)            evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)            evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)            evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)            evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)            evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 0)            koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.31/1.43	
2.31/1.43		start location:	koat_start
2.31/1.43	
2.31/1.43		leaf cost:	0
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	A polynomial rank function with
2.31/1.43	
2.31/1.43		Pol(evalt19start) = V_4 + 151
2.31/1.43	
2.31/1.43		Pol(evalt19bb0in) = V_4 + 151
2.31/1.43	
2.31/1.43		Pol(evalt19bb1in) = V_4 + 151
2.31/1.43	
2.31/1.43		Pol(evalt19bb2in) = V_4 + 151
2.31/1.43	
2.31/1.43		Pol(evalt19bb3in) = V_1 + V_4 + 51
2.31/1.43	
2.31/1.43		Pol(evalt19bb4in) = V_3 + 1
2.31/1.43	
2.31/1.43		Pol(evalt19bb5in) = V_3
2.31/1.43	
2.31/1.43		Pol(evalt19bb6in) = V_3
2.31/1.43	
2.31/1.43		Pol(evalt19stop) = V_3
2.31/1.43	
2.31/1.43		Pol(koat_start) = V_4 + 151
2.31/1.43	
2.31/1.43	orients all transitions weakly and the transition
2.31/1.43	
2.31/1.43		evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.31/1.43	
2.31/1.43	strictly and produces the following problem:
2.31/1.43	
2.31/1.43	6:	T:
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)             evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)             evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ar_1 + 51, Cost: 1)     evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)             evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
2.31/1.43	
2.31/1.43			(Comp: ar_1 + 51, Cost: 1)     evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)             evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ar_3 + 151, Cost: 1)    evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)             evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.31/1.43	
2.31/1.43			(Comp: ?, Cost: 1)             evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)             evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.31/1.43	
2.31/1.43		start location:	koat_start
2.31/1.43	
2.31/1.43		leaf cost:	0
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.31/1.43	
2.31/1.43	7:	T:
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)             evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 1)             evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ar_1 + 51, Cost: 1)     evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)             evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
2.31/1.43	
2.31/1.43			(Comp: ar_1 + 51, Cost: 1)     evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)             evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3))
2.31/1.43	
2.31/1.43			(Comp: ar_3 + 151, Cost: 1)    evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)             evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.31/1.43	
2.31/1.43			(Comp: ar_3 + 151, Cost: 1)    evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 4, Cost: 1)             evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3))
2.31/1.43	
2.31/1.43			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.31/1.43	
2.31/1.43		start location:	koat_start
2.31/1.43	
2.31/1.43		leaf cost:	0
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	Complexity upper bound 2*ar_1 + 2*ar_3 + 422
2.31/1.43	
2.31/1.43	
2.31/1.43	
2.31/1.43	Time: 0.131 sec (SMT: 0.115 sec)
2.31/1.43	
2.31/1.43	
2.31/1.43	----------------------------------------
2.31/1.43	
2.31/1.43	(2)
2.31/1.43	BOUNDS(1, n^1)
2.34/4.17	EOF