2.60/1.52	WORST_CASE(?, O(n^1))
2.61/1.53	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.61/1.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.61/1.53	
2.61/1.53	
2.61/1.53	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.61/1.53	
2.61/1.53	(0) CpxIntTrs
2.61/1.53	(1) Koat Proof [FINISHED, 278 ms]
2.61/1.53	(2) BOUNDS(1, n^1)
2.61/1.53	
2.61/1.53	
2.61/1.53	----------------------------------------
2.61/1.53	
2.61/1.53	(0)
2.61/1.53	Obligation:
2.61/1.53	Complexity Int TRS consisting of the following rules:
2.61/1.53	eval_t11_start(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_bb0_in(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: TRUE
2.61/1.53	eval_t11_bb0_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_bb1_in(v_x, v_y, v_m, v_n, v_x, v_y)) :|: TRUE
2.61/1.53	eval_t11_bb1_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: v_n > v_.0
2.61/1.53	eval_t11_bb1_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_bb3_in(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: v_n <= v_.0
2.61/1.53	eval_t11_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_bb1_in(v_.0, v_.01 + 1, v_m, v_n, v_x, v_y)) :|: v_m > v_.01
2.61/1.53	eval_t11_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_bb1_in(v_.0 + 1, v_.01 + 1, v_m, v_n, v_x, v_y)) :|: v_m > v_.01 && v_m <= v_.01
2.61/1.53	eval_t11_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_bb1_in(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: v_m <= v_.01 && v_m > v_.01
2.61/1.53	eval_t11_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_bb1_in(v_.0 + 1, v_.01, v_m, v_n, v_x, v_y)) :|: v_m <= v_.01
2.61/1.53	eval_t11_bb3_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_t11_stop(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: TRUE
2.61/1.53	
2.61/1.53	The start-symbols are:[eval_t11_start_6]
2.61/1.53	
2.61/1.53	
2.61/1.53	----------------------------------------
2.61/1.53	
2.61/1.53	(1) Koat Proof (FINISHED)
2.61/1.53	YES(?, 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 7)
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	Initial complexity problem:
2.61/1.53	
2.61/1.53	1:	T:
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 /\ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 /\ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.61/1.53	
2.61/1.53		start location:	koat_start
2.61/1.53	
2.61/1.53		leaf cost:	0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.61/1.53	
2.61/1.53		evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 /\ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53		evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 /\ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53	We thus obtain the following problem:
2.61/1.53	
2.61/1.53	2:	T:
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.61/1.53	
2.61/1.53		start location:	koat_start
2.61/1.53	
2.61/1.53		leaf cost:	0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.61/1.53	
2.61/1.53	3:	T:
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)    evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)    evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.61/1.53	
2.61/1.53		start location:	koat_start
2.61/1.53	
2.61/1.53		leaf cost:	0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	A polynomial rank function with
2.61/1.53	
2.61/1.53		Pol(evalt11bb3in) = 1
2.61/1.53	
2.61/1.53		Pol(evalt11stop) = 0
2.61/1.53	
2.61/1.53		Pol(evalt11bb2in) = 2
2.61/1.53	
2.61/1.53		Pol(evalt11bb1in) = 2
2.61/1.53	
2.61/1.53		Pol(evalt11bb0in) = 2
2.61/1.53	
2.61/1.53		Pol(evalt11start) = 2
2.61/1.53	
2.61/1.53		Pol(koat_start) = 2
2.61/1.53	
2.61/1.53	orients all transitions weakly and the transitions
2.61/1.53	
2.61/1.53		evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53		evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53	strictly and produces the following problem:
2.61/1.53	
2.61/1.53	4:	T:
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)    evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)    evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)    evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.61/1.53	
2.61/1.53		start location:	koat_start
2.61/1.53	
2.61/1.53		leaf cost:	0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	A polynomial rank function with
2.61/1.53	
2.61/1.53		Pol(evalt11bb3in) = -V_3 + V_6
2.61/1.53	
2.61/1.53		Pol(evalt11stop) = -V_3 + V_6
2.61/1.53	
2.61/1.53		Pol(evalt11bb2in) = -V_3 + V_6
2.61/1.53	
2.61/1.53		Pol(evalt11bb1in) = -V_3 + V_6
2.61/1.53	
2.61/1.53		Pol(evalt11bb0in) = -V_4 + V_6
2.61/1.53	
2.61/1.53		Pol(evalt11start) = -V_4 + V_6
2.61/1.53	
2.61/1.53		Pol(koat_start) = -V_4 + V_6
2.61/1.53	
2.61/1.53	orients all transitions weakly and the transition
2.61/1.53	
2.61/1.53		evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53	strictly and produces the following problem:
2.61/1.53	
2.61/1.53	5:	T:
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)              evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)              evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: ar_3 + ar_5, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)              evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)              evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)              evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)              evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.61/1.53	
2.61/1.53		start location:	koat_start
2.61/1.53	
2.61/1.53		leaf cost:	0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	Applied AI with 'oct' on problem 5 to obtain the following invariants:
2.61/1.53	
2.61/1.53	  For symbol evalt11bb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.61/1.53	
2.61/1.53	  For symbol evalt11bb2in: -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.61/1.53	
2.61/1.53	  For symbol evalt11bb3in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	This yielded the following problem:
2.61/1.53	
2.61/1.53	6:	T:
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)              evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)              evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)              evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)              evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53			(Comp: ar_3 + ar_5, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)              evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)              evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.61/1.53	
2.61/1.53		start location:	koat_start
2.61/1.53	
2.61/1.53		leaf cost:	0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	A polynomial rank function with
2.61/1.53	
2.61/1.53		Pol(koat_start) = -V_2 + V_5
2.61/1.53	
2.61/1.53		Pol(evalt11start) = -V_2 + V_5
2.61/1.53	
2.61/1.53		Pol(evalt11bb0in) = -V_2 + V_5
2.61/1.53	
2.61/1.53		Pol(evalt11bb1in) = -V_1 + V_5
2.61/1.53	
2.61/1.53		Pol(evalt11bb2in) = -V_1 + V_5
2.61/1.53	
2.61/1.53		Pol(evalt11bb3in) = -V_1 + V_5
2.61/1.53	
2.61/1.53		Pol(evalt11stop) = -V_1 + V_5
2.61/1.53	
2.61/1.53	orients all transitions weakly and the transition
2.61/1.53	
2.61/1.53		evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53	strictly and produces the following problem:
2.61/1.53	
2.61/1.53	7:	T:
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)              evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)              evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ?, Cost: 1)              evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)              evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53			(Comp: ar_3 + ar_5, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ar_1 + ar_4, Cost: 1)    evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)              evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.61/1.53	
2.61/1.53		start location:	koat_start
2.61/1.53	
2.61/1.53		leaf cost:	0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.61/1.53	
2.61/1.53	8:	T:
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 0)                                koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)                                evalt11start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: 1, Cost: 1)                                evalt11bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))
2.61/1.53	
2.61/1.53			(Comp: ar_1 + ar_4 + ar_3 + ar_5 + 1, Cost: 1)    evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)                                evalt11bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ]
2.61/1.53	
2.61/1.53			(Comp: ar_3 + ar_5, Cost: 1)                      evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ]
2.61/1.53	
2.61/1.53			(Comp: ar_1 + ar_4, Cost: 1)                      evalt11bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ]
2.61/1.53	
2.61/1.53			(Comp: 2, Cost: 1)                                evalt11bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt11stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ]
2.61/1.53	
2.61/1.53		start location:	koat_start
2.61/1.53	
2.61/1.53		leaf cost:	0
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	Complexity upper bound 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 7
2.61/1.53	
2.61/1.53	
2.61/1.53	
2.61/1.53	Time: 0.252 sec (SMT: 0.211 sec)
2.61/1.53	
2.61/1.53	
2.61/1.53	----------------------------------------
2.61/1.53	
2.61/1.53	(2)
2.61/1.53	BOUNDS(1, n^1)
2.61/1.54	EOF