380.25/291.60	WORST_CASE(Omega(n^1), O(n^2))
380.25/291.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
380.25/291.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
380.25/291.61	
380.25/291.61	
380.25/291.61	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
380.25/291.61	
380.25/291.61	(0) CpxTRS
380.25/291.61	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
380.25/291.61	(2) CpxWeightedTrs
380.25/291.61	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
380.25/291.61	    (4) CpxTypedWeightedTrs
380.25/291.61	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (6) CpxTypedWeightedCompleteTrs
380.25/291.61	    (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
380.25/291.61	    (8) CpxTypedWeightedCompleteTrs
380.25/291.61	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (10) CpxRNTS
380.25/291.61	    (11) InliningProof [UPPER BOUND(ID), 853 ms]
380.25/291.61	    (12) CpxRNTS
380.25/291.61	    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
380.25/291.61	    (14) CpxRNTS
380.25/291.61	    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
380.25/291.61	    (16) CpxRNTS
380.25/291.61	    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (18) CpxRNTS
380.25/291.61	    (19) IntTrsBoundProof [UPPER BOUND(ID), 263 ms]
380.25/291.61	    (20) CpxRNTS
380.25/291.61	    (21) IntTrsBoundProof [UPPER BOUND(ID), 75 ms]
380.25/291.61	    (22) CpxRNTS
380.25/291.61	    (23) ResultPropagationProof [UPPER BOUND(ID), 3 ms]
380.25/291.61	    (24) CpxRNTS
380.25/291.61	    (25) IntTrsBoundProof [UPPER BOUND(ID), 373 ms]
380.25/291.61	    (26) CpxRNTS
380.25/291.61	    (27) IntTrsBoundProof [UPPER BOUND(ID), 125 ms]
380.25/291.61	    (28) CpxRNTS
380.25/291.61	    (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (30) CpxRNTS
380.25/291.61	    (31) IntTrsBoundProof [UPPER BOUND(ID), 148 ms]
380.25/291.61	    (32) CpxRNTS
380.25/291.61	    (33) IntTrsBoundProof [UPPER BOUND(ID), 22 ms]
380.25/291.61	    (34) CpxRNTS
380.25/291.61	    (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (36) CpxRNTS
380.25/291.61	    (37) IntTrsBoundProof [UPPER BOUND(ID), 329 ms]
380.25/291.61	    (38) CpxRNTS
380.25/291.61	    (39) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
380.25/291.61	    (40) CpxRNTS
380.25/291.61	    (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (42) CpxRNTS
380.25/291.61	    (43) IntTrsBoundProof [UPPER BOUND(ID), 260 ms]
380.25/291.61	    (44) CpxRNTS
380.25/291.61	    (45) IntTrsBoundProof [UPPER BOUND(ID), 125 ms]
380.25/291.61	    (46) CpxRNTS
380.25/291.61	    (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (48) CpxRNTS
380.25/291.61	    (49) IntTrsBoundProof [UPPER BOUND(ID), 2233 ms]
380.25/291.61	    (50) CpxRNTS
380.25/291.61	    (51) IntTrsBoundProof [UPPER BOUND(ID), 1221 ms]
380.25/291.61	    (52) CpxRNTS
380.25/291.61	    (53) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (54) CpxRNTS
380.25/291.61	    (55) IntTrsBoundProof [UPPER BOUND(ID), 1303 ms]
380.25/291.61	    (56) CpxRNTS
380.25/291.61	    (57) IntTrsBoundProof [UPPER BOUND(ID), 1065 ms]
380.25/291.61	    (58) CpxRNTS
380.25/291.61	    (59) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (60) CpxRNTS
380.25/291.61	    (61) IntTrsBoundProof [UPPER BOUND(ID), 395 ms]
380.25/291.61	    (62) CpxRNTS
380.25/291.61	    (63) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
380.25/291.61	    (64) CpxRNTS
380.25/291.61	    (65) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
380.25/291.61	    (66) CpxRNTS
380.25/291.61	    (67) IntTrsBoundProof [UPPER BOUND(ID), 258 ms]
380.25/291.61	    (68) CpxRNTS
380.25/291.61	    (69) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
380.25/291.61	    (70) CpxRNTS
380.25/291.61	    (71) FinalProof [FINISHED, 0 ms]
380.25/291.61	    (72) BOUNDS(1, n^2)
380.25/291.61	(73) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
380.25/291.61	(74) TRS for Loop Detection
380.25/291.61	    (75) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
380.25/291.61	    (76) BEST
380.25/291.61	        (77) proven lower bound
380.25/291.61	            (78) LowerBoundPropagationProof [FINISHED, 0 ms]
380.25/291.61	            (79) BOUNDS(n^1, INF)
380.25/291.61	        (80) TRS for Loop Detection
380.25/291.61	
380.25/291.61	
380.25/291.61	----------------------------------------
380.25/291.61	
380.25/291.61	(0)
380.25/291.61	Obligation:
380.25/291.61	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
380.25/291.61	
380.25/291.61	
380.25/291.61	The TRS R consists of the following rules:
380.25/291.61	
380.25/291.61	   if(true, t, e) -> t
380.25/291.61	   if(false, t, e) -> e
380.25/291.61	   member(x, nil) -> false
380.25/291.61	   member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys))
380.25/291.61	   eq(nil, nil) -> true
380.25/291.61	   eq(O(x), 0(y)) -> eq(x, y)
380.25/291.61	   eq(0(x), 1(y)) -> false
380.25/291.61	   eq(1(x), 0(y)) -> false
380.25/291.61	   eq(1(x), 1(y)) -> eq(x, y)
380.25/291.61	   negate(0(x)) -> 1(x)
380.25/291.61	   negate(1(x)) -> 0(x)
380.25/291.61	   choice(cons(x, xs)) -> x
380.25/291.61	   choice(cons(x, xs)) -> choice(xs)
380.25/291.61	   guess(nil) -> nil
380.25/291.61	   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf))
380.25/291.61	   verify(nil) -> true
380.25/291.61	   verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls))
380.25/291.61	   sat(cnf) -> satck(cnf, guess(cnf))
380.25/291.61	   satck(cnf, assign) -> if(verify(assign), assign, unsat)
380.25/291.61	
380.25/291.61	S is empty.
380.25/291.61	Rewrite Strategy: INNERMOST
380.25/291.61	----------------------------------------
380.25/291.61	
380.25/291.61	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
380.25/291.61	Transformed relative TRS to weighted TRS
380.25/291.61	----------------------------------------
380.25/291.61	
380.25/291.61	(2)
380.25/291.61	Obligation:
380.25/291.61	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).
380.25/291.61	
380.25/291.61	
380.25/291.61	The TRS R consists of the following rules:
380.25/291.61	
380.25/291.61	   if(true, t, e) -> t [1]
380.25/291.61	   if(false, t, e) -> e [1]
380.25/291.61	   member(x, nil) -> false [1]
380.25/291.61	   member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys)) [1]
380.25/291.61	   eq(nil, nil) -> true [1]
380.25/291.61	   eq(O(x), 0(y)) -> eq(x, y) [1]
380.25/291.61	   eq(0(x), 1(y)) -> false [1]
380.25/291.61	   eq(1(x), 0(y)) -> false [1]
380.25/291.61	   eq(1(x), 1(y)) -> eq(x, y) [1]
380.25/291.61	   negate(0(x)) -> 1(x) [1]
380.25/291.61	   negate(1(x)) -> 0(x) [1]
380.25/291.61	   choice(cons(x, xs)) -> x [1]
380.25/291.61	   choice(cons(x, xs)) -> choice(xs) [1]
380.25/291.61	   guess(nil) -> nil [1]
380.25/291.61	   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf)) [1]
380.25/291.61	   verify(nil) -> true [1]
380.25/291.61	   verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls)) [1]
380.25/291.61	   sat(cnf) -> satck(cnf, guess(cnf)) [1]
380.25/291.61	   satck(cnf, assign) -> if(verify(assign), assign, unsat) [1]
380.25/291.61	
380.25/291.61	Rewrite Strategy: INNERMOST
380.25/291.61	----------------------------------------
380.25/291.61	
380.25/291.61	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
380.25/291.61	Infered types.
380.25/291.61	----------------------------------------
380.25/291.61	
380.25/291.61	(4)
380.25/291.61	Obligation:
380.25/291.61	Runtime Complexity Weighted TRS with Types.
380.25/291.61	The TRS R consists of the following rules:
380.25/291.61	
380.25/291.61	   if(true, t, e) -> t [1]
380.25/291.61	   if(false, t, e) -> e [1]
380.25/291.61	   member(x, nil) -> false [1]
380.25/291.61	   member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys)) [1]
380.25/291.61	   eq(nil, nil) -> true [1]
380.25/291.61	   eq(O(x), 0(y)) -> eq(x, y) [1]
380.25/291.61	   eq(0(x), 1(y)) -> false [1]
380.25/291.61	   eq(1(x), 0(y)) -> false [1]
380.25/291.61	   eq(1(x), 1(y)) -> eq(x, y) [1]
380.25/291.61	   negate(0(x)) -> 1(x) [1]
380.25/291.61	   negate(1(x)) -> 0(x) [1]
380.25/291.61	   choice(cons(x, xs)) -> x [1]
380.25/291.61	   choice(cons(x, xs)) -> choice(xs) [1]
380.25/291.61	   guess(nil) -> nil [1]
380.25/291.61	   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf)) [1]
380.25/291.61	   verify(nil) -> true [1]
380.25/291.61	   verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls)) [1]
380.25/291.61	   sat(cnf) -> satck(cnf, guess(cnf)) [1]
380.25/291.61	   satck(cnf, assign) -> if(verify(assign), assign, unsat) [1]
380.25/291.61	
380.25/291.61	The TRS has the following type information:
380.25/291.61	if :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	true :: true:false:nil:cons:O:0:1:unsat
380.25/291.61	false :: true:false:nil:cons:O:0:1:unsat
380.25/291.61	member :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	nil :: true:false:nil:cons:O:0:1:unsat
380.25/291.61	cons :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	eq :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	O :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	0 :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	1 :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	negate :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	choice :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	guess :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	verify :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	sat :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	satck :: true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat -> true:false:nil:cons:O:0:1:unsat
380.25/291.61	unsat :: true:false:nil:cons:O:0:1:unsat
380.25/291.61	
380.25/291.61	Rewrite Strategy: INNERMOST
380.25/291.61	----------------------------------------
380.25/291.61	
380.25/291.61	(5) CompletionProof (UPPER BOUND(ID))
380.25/291.61	The transformation into a RNTS is sound, since:
380.25/291.61	
380.25/291.61	(a) The obligation is a constructor system where every type has a constant constructor,
380.25/291.61	
380.25/291.61	(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
380.25/291.61	
380.25/291.61	   sat_1
380.25/291.61	   satck_2
380.25/291.61	
380.25/291.61	(c) The following functions are completely defined:
380.25/291.61	
380.25/291.61	   verify_1
380.25/291.61	   member_2
380.25/291.61	   negate_1
380.25/291.61	   eq_2
380.25/291.61	   guess_1
380.25/291.61	   if_3
380.25/291.61	   choice_1
380.25/291.61	
380.25/291.61	Due to the following rules being added:
380.25/291.61	
380.25/291.61	   verify(v0) -> null_verify [0]
380.25/291.61	   member(v0, v1) -> null_member [0]
380.25/291.62	   negate(v0) -> null_negate [0]
380.25/291.62	   eq(v0, v1) -> null_eq [0]
380.25/291.62	   guess(v0) -> null_guess [0]
380.25/291.62	   if(v0, v1, v2) -> null_if [0]
380.25/291.62	   choice(v0) -> null_choice [0]
380.25/291.62	
380.25/291.62	And the following fresh constants:    null_verify, null_member, null_negate, null_eq, null_guess, null_if, null_choice
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(6)
380.25/291.62	Obligation:
380.25/291.62	Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:
380.25/291.62	
380.25/291.62	Runtime Complexity Weighted TRS with Types.
380.25/291.62	The TRS R consists of the following rules:
380.25/291.62	
380.25/291.62	   if(true, t, e) -> t [1]
380.25/291.62	   if(false, t, e) -> e [1]
380.25/291.62	   member(x, nil) -> false [1]
380.25/291.62	   member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys)) [1]
380.25/291.62	   eq(nil, nil) -> true [1]
380.25/291.62	   eq(O(x), 0(y)) -> eq(x, y) [1]
380.25/291.62	   eq(0(x), 1(y)) -> false [1]
380.25/291.62	   eq(1(x), 0(y)) -> false [1]
380.25/291.62	   eq(1(x), 1(y)) -> eq(x, y) [1]
380.25/291.62	   negate(0(x)) -> 1(x) [1]
380.25/291.62	   negate(1(x)) -> 0(x) [1]
380.25/291.62	   choice(cons(x, xs)) -> x [1]
380.25/291.62	   choice(cons(x, xs)) -> choice(xs) [1]
380.25/291.62	   guess(nil) -> nil [1]
380.25/291.62	   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf)) [1]
380.25/291.62	   verify(nil) -> true [1]
380.25/291.62	   verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls)) [1]
380.25/291.62	   sat(cnf) -> satck(cnf, guess(cnf)) [1]
380.25/291.62	   satck(cnf, assign) -> if(verify(assign), assign, unsat) [1]
380.25/291.62	   verify(v0) -> null_verify [0]
380.25/291.62	   member(v0, v1) -> null_member [0]
380.25/291.62	   negate(v0) -> null_negate [0]
380.25/291.62	   eq(v0, v1) -> null_eq [0]
380.25/291.62	   guess(v0) -> null_guess [0]
380.25/291.62	   if(v0, v1, v2) -> null_if [0]
380.25/291.62	   choice(v0) -> null_choice [0]
380.25/291.62	
380.25/291.62	The TRS has the following type information:
380.25/291.62	if :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	true :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	false :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	member :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	nil :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	cons :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	eq :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	O :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	0 :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	1 :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	negate :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	choice :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	guess :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	verify :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	sat :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	satck :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	unsat :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_verify :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_member :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_negate :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_eq :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_guess :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_if :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_choice :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	
380.25/291.62	Rewrite Strategy: INNERMOST
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(7) NarrowingProof (BOTH BOUNDS(ID, ID))
380.25/291.62	Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(8)
380.25/291.62	Obligation:
380.25/291.62	Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:
380.25/291.62	
380.25/291.62	Runtime Complexity Weighted TRS with Types.
380.25/291.62	The TRS R consists of the following rules:
380.25/291.62	
380.25/291.62	   if(true, t, e) -> t [1]
380.25/291.62	   if(false, t, e) -> e [1]
380.25/291.62	   member(x, nil) -> false [1]
380.25/291.62	   member(nil, cons(nil, nil)) -> if(true, true, false) [3]
380.25/291.62	   member(nil, cons(nil, cons(y3, ys'))) -> if(true, true, if(eq(nil, y3), true, member(nil, ys'))) [3]
380.25/291.62	   member(nil, cons(nil, ys)) -> if(true, true, null_member) [2]
380.25/291.62	   member(O(x'), cons(0(y'), nil)) -> if(eq(x', y'), true, false) [3]
380.25/291.62	   member(O(x'), cons(0(y'), cons(y4, ys''))) -> if(eq(x', y'), true, if(eq(O(x'), y4), true, member(O(x'), ys''))) [3]
380.25/291.62	   member(O(x'), cons(0(y'), ys)) -> if(eq(x', y'), true, null_member) [2]
380.25/291.62	   member(0(x''), cons(1(y''), nil)) -> if(false, true, false) [3]
380.25/291.62	   member(0(x''), cons(1(y''), cons(y5, ys1))) -> if(false, true, if(eq(0(x''), y5), true, member(0(x''), ys1))) [3]
380.25/291.62	   member(0(x''), cons(1(y''), ys)) -> if(false, true, null_member) [2]
380.25/291.62	   member(1(x1), cons(0(y1), nil)) -> if(false, true, false) [3]
380.25/291.62	   member(1(x1), cons(0(y1), cons(y6, ys2))) -> if(false, true, if(eq(1(x1), y6), true, member(1(x1), ys2))) [3]
380.25/291.62	   member(1(x1), cons(0(y1), ys)) -> if(false, true, null_member) [2]
380.25/291.62	   member(1(x2), cons(1(y2), nil)) -> if(eq(x2, y2), true, false) [3]
380.25/291.62	   member(1(x2), cons(1(y2), cons(y7, ys3))) -> if(eq(x2, y2), true, if(eq(1(x2), y7), true, member(1(x2), ys3))) [3]
380.25/291.62	   member(1(x2), cons(1(y2), ys)) -> if(eq(x2, y2), true, null_member) [2]
380.25/291.62	   member(x, cons(y, nil)) -> if(null_eq, true, false) [2]
380.25/291.62	   member(x, cons(y, cons(y8, ys4))) -> if(null_eq, true, if(eq(x, y8), true, member(x, ys4))) [2]
380.25/291.62	   member(x, cons(y, ys)) -> if(null_eq, true, null_member) [1]
380.25/291.62	   eq(nil, nil) -> true [1]
380.25/291.62	   eq(O(x), 0(y)) -> eq(x, y) [1]
380.25/291.62	   eq(0(x), 1(y)) -> false [1]
380.25/291.62	   eq(1(x), 0(y)) -> false [1]
380.25/291.62	   eq(1(x), 1(y)) -> eq(x, y) [1]
380.25/291.62	   negate(0(x)) -> 1(x) [1]
380.25/291.62	   negate(1(x)) -> 0(x) [1]
380.25/291.62	   choice(cons(x, xs)) -> x [1]
380.25/291.62	   choice(cons(x, xs)) -> choice(xs) [1]
380.25/291.62	   guess(nil) -> nil [1]
380.25/291.62	   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf)) [1]
380.25/291.62	   verify(nil) -> true [1]
380.25/291.62	   verify(cons(0(x3), nil)) -> if(member(1(x3), nil), false, true) [3]
380.25/291.62	   verify(cons(0(x3), cons(l', ls'))) -> if(member(1(x3), cons(l', ls')), false, if(member(negate(l'), ls'), false, verify(ls'))) [3]
380.25/291.62	   verify(cons(0(x3), ls)) -> if(member(1(x3), ls), false, null_verify) [2]
380.25/291.62	   verify(cons(1(x4), nil)) -> if(member(0(x4), nil), false, true) [3]
380.25/291.62	   verify(cons(1(x4), cons(l'', ls''))) -> if(member(0(x4), cons(l'', ls'')), false, if(member(negate(l''), ls''), false, verify(ls''))) [3]
380.25/291.62	   verify(cons(1(x4), ls)) -> if(member(0(x4), ls), false, null_verify) [2]
380.25/291.62	   verify(cons(l, nil)) -> if(member(null_negate, nil), false, true) [2]
380.25/291.62	   verify(cons(l, cons(l1, ls1))) -> if(member(null_negate, cons(l1, ls1)), false, if(member(negate(l1), ls1), false, verify(ls1))) [2]
380.25/291.62	   verify(cons(l, ls)) -> if(member(null_negate, ls), false, null_verify) [1]
380.25/291.62	   sat(nil) -> satck(nil, nil) [2]
380.25/291.62	   sat(cons(clause', cnf')) -> satck(cons(clause', cnf'), cons(choice(clause'), guess(cnf'))) [2]
380.25/291.62	   sat(cnf) -> satck(cnf, null_guess) [1]
380.25/291.62	   satck(cnf, nil) -> if(true, nil, unsat) [2]
380.25/291.62	   satck(cnf, cons(l2, ls2)) -> if(if(member(negate(l2), ls2), false, verify(ls2)), cons(l2, ls2), unsat) [2]
380.25/291.62	   satck(cnf, assign) -> if(null_verify, assign, unsat) [1]
380.25/291.62	   verify(v0) -> null_verify [0]
380.25/291.62	   member(v0, v1) -> null_member [0]
380.25/291.62	   negate(v0) -> null_negate [0]
380.25/291.62	   eq(v0, v1) -> null_eq [0]
380.25/291.62	   guess(v0) -> null_guess [0]
380.25/291.62	   if(v0, v1, v2) -> null_if [0]
380.25/291.62	   choice(v0) -> null_choice [0]
380.25/291.62	
380.25/291.62	The TRS has the following type information:
380.25/291.62	if :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	true :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	false :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	member :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	nil :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	cons :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	eq :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	O :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	0 :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	1 :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	negate :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	choice :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	guess :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	verify :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	sat :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	satck :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice -> true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	unsat :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_verify :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_member :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_negate :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_eq :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_guess :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_if :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	null_choice :: true:false:nil:cons:O:0:1:unsat:null_verify:null_member:null_negate:null_eq:null_guess:null_if:null_choice
380.25/291.62	
380.25/291.62	Rewrite Strategy: INNERMOST
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(9) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
380.25/291.62	Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
380.25/291.62	The constant constructors are abstracted as follows:
380.25/291.62	
380.25/291.62	   true => 2
380.25/291.62	   false => 0
380.25/291.62	   nil => 1
380.25/291.62	   unsat => 3
380.25/291.62	   null_verify => 0
380.25/291.62	   null_member => 0
380.25/291.62	   null_negate => 0
380.25/291.62	   null_eq => 0
380.25/291.62	   null_guess => 0
380.25/291.62	   null_if => 0
380.25/291.62	   null_choice => 0
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(10)
380.25/291.62	Obligation:
380.25/291.62	Complexity RNTS consisting of the following rules:
380.25/291.62	
380.25/291.62	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 1 }-> choice(xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	   eq(z, z') -{ 1 }-> eq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
380.25/291.62	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.62	   eq(z, z') -{ 1 }-> 0 :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
380.25/291.62	   eq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
380.25/291.62	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.62	   guess(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	   guess(z) -{ 1 }-> 1 + choice(clause) + guess(cnf) :|: cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> e :|: z' = t, t >= 0, e >= 0, z = 0, z'' = e
380.25/291.62	   if(z, z', z'') -{ 1 }-> t :|: z = 2, z' = t, t >= 0, e >= 0, z'' = e
380.25/291.62	   if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(x', y'), 2, if(eq(1 + x', y4), 2, member(1 + x', ys''))) :|: z = 1 + x', z' = 1 + (1 + y') + (1 + y4 + ys''), x' >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(x', y'), 2, 0) :|: z = 1 + x', x' >= 0, y' >= 0, z' = 1 + (1 + y') + 1
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(x', y'), 2, 0) :|: z = 1 + x', z' = 1 + (1 + y') + ys, ys >= 0, x' >= 0, y' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(x2, y2), 2, if(eq(1 + x2, y7), 2, member(1 + x2, ys3))) :|: z = 1 + x2, y7 >= 0, ys3 >= 0, y2 >= 0, x2 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(x2, y2), 2, 0) :|: z = 1 + x2, z' = 1 + (1 + y2) + 1, y2 >= 0, x2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(x2, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, z = 1 + x2, y2 >= 0, x2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(2, 2, 0) :|: z' = 1 + 1 + 1, z = 1
380.25/291.62	   member(z, z') -{ 2 }-> if(2, 2, 0) :|: z = 1, ys >= 0, z' = 1 + 1 + ys
380.25/291.62	   member(z, z') -{ 2 }-> if(0, 2, if(eq(x, y8), 2, member(x, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, x >= 0, y >= 0, ys4 >= 0, z = x
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + x'', y5), 2, member(1 + x'', ys1))) :|: z = 1 + x'', y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, x'' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + x1, y6), 2, member(1 + x1, ys2))) :|: y1 >= 0, x1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, z = 1 + x1, ys2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, 0) :|: z = 1 + x'', z' = 1 + (1 + y'') + 1, y'' >= 0, x'' >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(0, 2, 0) :|: z = 1 + x'', z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, x'' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, 0) :|: y1 >= 0, x1 >= 0, z' = 1 + (1 + y1) + 1, z = 1 + x1
380.25/291.62	   member(z, z') -{ 2 }-> if(0, 2, 0) :|: y1 >= 0, x1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, z = 1 + x1
380.25/291.62	   member(z, z') -{ 2 }-> if(0, 2, 0) :|: z' = 1 + y + 1, x >= 0, y >= 0, z = x
380.25/291.62	   member(z, z') -{ 1 }-> if(0, 2, 0) :|: ys >= 0, x >= 0, y >= 0, z = x, z' = 1 + y + ys
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: x >= 0, z' = 1, z = x
380.25/291.62	   member(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
380.25/291.62	   negate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	   negate(z) -{ 1 }-> 1 + x :|: x >= 0, z = 1 + x
380.25/291.62	   sat(z) -{ 1 }-> satck(cnf, 0) :|: cnf >= 0, z = cnf
380.25/291.62	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.62	   sat(z) -{ 2 }-> satck(1 + clause' + cnf', 1 + choice(clause') + guess(cnf')) :|: clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.62	   satck(z, z') -{ 2 }-> if(if(member(negate(l2), ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, cnf >= 0, z = cnf, l2 >= 0, ls2 >= 0
380.25/291.62	   satck(z, z') -{ 2 }-> if(2, 1, 3) :|: cnf >= 0, z' = 1, z = cnf
380.25/291.62	   satck(z, z') -{ 1 }-> if(0, assign, 3) :|: cnf >= 0, z' = assign, z = cnf, assign >= 0
380.25/291.62	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z = 1 + l + 1, l >= 0
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(negate(l1), ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x3, 1), 0, 2) :|: z = 1 + (1 + x3) + 1, x3 >= 0
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(negate(l'), ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x4, 1), 0, 2) :|: x4 >= 0, z = 1 + (1 + x4) + 1
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(negate(l''), ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0
380.25/291.62	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.62	   verify(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(11) InliningProof (UPPER BOUND(ID))
380.25/291.62	Inlined the following terminating rules on right-hand sides where appropriate:
380.25/291.62	
380.25/291.62	   if(z, z', z'') -{ 1 }-> e :|: z' = t, t >= 0, e >= 0, z = 0, z'' = e
380.25/291.62	   if(z, z', z'') -{ 1 }-> t :|: z = 2, z' = t, t >= 0, e >= 0, z'' = e
380.25/291.62	   if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
380.25/291.62	   negate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	   negate(z) -{ 1 }-> 1 + x :|: x >= 0, z = 1 + x
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(12)
380.25/291.62	Obligation:
380.25/291.62	Complexity RNTS consisting of the following rules:
380.25/291.62	
380.25/291.62	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 1 }-> choice(xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	   eq(z, z') -{ 1 }-> eq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
380.25/291.62	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.62	   eq(z, z') -{ 1 }-> 0 :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
380.25/291.62	   eq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
380.25/291.62	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.62	   guess(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	   guess(z) -{ 1 }-> 1 + choice(clause) + guess(cnf) :|: cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> e :|: z' = t, t >= 0, e >= 0, z = 0, z'' = e
380.25/291.62	   if(z, z', z'') -{ 1 }-> t :|: z = 2, z' = t, t >= 0, e >= 0, z'' = e
380.25/291.62	   if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 4 }-> e :|: z = 1 + x'', z' = 1 + (1 + y'') + 1, y'' >= 0, x'' >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z = 1 + x'', z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, x'' >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 4 }-> e :|: y1 >= 0, x1 >= 0, z' = 1 + (1 + y1) + 1, z = 1 + x1, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: y1 >= 0, x1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, z = 1 + x1, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z' = 1 + y + 1, x >= 0, y >= 0, z = x, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 2 }-> e :|: ys >= 0, x >= 0, y >= 0, z = x, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> t :|: z = 1, ys >= 0, z' = 1 + 1 + ys, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(x', y'), 2, if(eq(1 + x', y4), 2, member(1 + x', ys''))) :|: z = 1 + x', z' = 1 + (1 + y') + (1 + y4 + ys''), x' >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(x', y'), 2, 0) :|: z = 1 + x', x' >= 0, y' >= 0, z' = 1 + (1 + y') + 1
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(x', y'), 2, 0) :|: z = 1 + x', z' = 1 + (1 + y') + ys, ys >= 0, x' >= 0, y' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(x2, y2), 2, if(eq(1 + x2, y7), 2, member(1 + x2, ys3))) :|: z = 1 + x2, y7 >= 0, ys3 >= 0, y2 >= 0, x2 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(x2, y2), 2, 0) :|: z = 1 + x2, z' = 1 + (1 + y2) + 1, y2 >= 0, x2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(x2, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, z = 1 + x2, y2 >= 0, x2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(0, 2, if(eq(x, y8), 2, member(x, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, x >= 0, y >= 0, ys4 >= 0, z = x
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + x'', y5), 2, member(1 + x'', ys1))) :|: z = 1 + x'', y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, x'' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + x1, y6), 2, member(1 + x1, ys2))) :|: y1 >= 0, x1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, z = 1 + x1, ys2 >= 0
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: x >= 0, z' = 1, z = x
380.25/291.62	   member(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z = 1, ys >= 0, z' = 1 + 1 + ys, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: z = 1 + x'', z' = 1 + (1 + y'') + 1, y'' >= 0, x'' >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z = 1 + x'', z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, x'' >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: y1 >= 0, x1 >= 0, z' = 1 + (1 + y1) + 1, z = 1 + x1, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, x1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, z = 1 + x1, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + y + 1, x >= 0, y >= 0, z = x, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, x >= 0, y >= 0, z = x, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   negate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	   negate(z) -{ 1 }-> 1 + x :|: x >= 0, z = 1 + x
380.25/291.62	   sat(z) -{ 1 }-> satck(cnf, 0) :|: cnf >= 0, z = cnf
380.25/291.62	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.62	   sat(z) -{ 2 }-> satck(1 + clause' + cnf', 1 + choice(clause') + guess(cnf')) :|: clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.62	   satck(z, z') -{ 2 }-> e :|: cnf >= 0, z' = assign, z = cnf, assign >= 0, assign = t, t >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.62	   satck(z, z') -{ 3 }-> t :|: cnf >= 0, z' = 1, z = cnf, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.62	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, cnf >= 0, z = cnf, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.62	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, cnf >= 0, z = cnf, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.62	   satck(z, z') -{ 2 }-> 0 :|: cnf >= 0, z' = 1, z = cnf, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.62	   satck(z, z') -{ 1 }-> 0 :|: cnf >= 0, z' = assign, z = cnf, assign >= 0, v0 >= 0, 3 = v2, v1 >= 0, 0 = v0, assign = v1, v2 >= 0
380.25/291.62	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z = 1 + l + 1, l >= 0
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.62	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x3, 1), 0, 2) :|: z = 1 + (1 + x3) + 1, x3 >= 0
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.62	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x4, 1), 0, 2) :|: x4 >= 0, z = 1 + (1 + x4) + 1
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.62	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.62	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.62	   verify(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
380.25/291.62	
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(13) SimplificationProof (BOTH BOUNDS(ID, ID))
380.25/291.62	Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(14)
380.25/291.62	Obligation:
380.25/291.62	Complexity RNTS consisting of the following rules:
380.25/291.62	
380.25/291.62	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 1 }-> choice(xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.62	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.62	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.62	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.62	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.62	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   guess(z) -{ 1 }-> 1 + choice(clause) + guess(cnf) :|: cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.62	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.62	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, y'), 2, if(eq(1 + (z - 1), y4), 2, member(1 + (z - 1), ys''))) :|: z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(z - 1, y'), 2, 0) :|: z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, y2), 2, if(eq(1 + (z - 1), y7), 2, member(1 + (z - 1), ys3))) :|: y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(z - 1, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, z' - 3), 2, 0) :|: z - 1 >= 0, z' - 3 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(0, 2, if(eq(z, y8), 2, member(z, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y5), 2, member(1 + (z - 1), ys1))) :|: y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y6), 2, member(1 + (z - 1), ys2))) :|: y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.62	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.62	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.62	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.62	   sat(z) -{ 2 }-> satck(1 + clause' + cnf', 1 + choice(clause') + guess(cnf')) :|: clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.62	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.62	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.62	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.62	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.62	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.62	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.62	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.62	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.62	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.62	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.62	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.62	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(15) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
380.25/291.62	Found the following analysis order by SCC decomposition:
380.25/291.62	
380.25/291.62	   { choice }
380.25/291.62	   { eq }
380.25/291.62	   { negate }
380.25/291.62	   { if }
380.25/291.62	   { guess }
380.25/291.62	   { member }
380.25/291.62	   { verify }
380.25/291.62	   { satck }
380.25/291.62	   { sat }
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(16)
380.25/291.62	Obligation:
380.25/291.62	Complexity RNTS consisting of the following rules:
380.25/291.62	
380.25/291.62	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 1 }-> choice(xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.62	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.62	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.62	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.62	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.62	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   guess(z) -{ 1 }-> 1 + choice(clause) + guess(cnf) :|: cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.62	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.62	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, y'), 2, if(eq(1 + (z - 1), y4), 2, member(1 + (z - 1), ys''))) :|: z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(z - 1, y'), 2, 0) :|: z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, y2), 2, if(eq(1 + (z - 1), y7), 2, member(1 + (z - 1), ys3))) :|: y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(z - 1, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, z' - 3), 2, 0) :|: z - 1 >= 0, z' - 3 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(0, 2, if(eq(z, y8), 2, member(z, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y5), 2, member(1 + (z - 1), ys1))) :|: y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y6), 2, member(1 + (z - 1), ys2))) :|: y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.62	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.62	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.62	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.62	   sat(z) -{ 2 }-> satck(1 + clause' + cnf', 1 + choice(clause') + guess(cnf')) :|: clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.62	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.62	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.62	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.62	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.62	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.62	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.62	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.62	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.62	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.62	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.62	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.62	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	
380.25/291.62	Function symbols to be analyzed: {choice}, {eq}, {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(17) ResultPropagationProof (UPPER BOUND(ID))
380.25/291.62	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(18)
380.25/291.62	Obligation:
380.25/291.62	Complexity RNTS consisting of the following rules:
380.25/291.62	
380.25/291.62	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 1 }-> choice(xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.62	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.62	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.62	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.62	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.62	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   guess(z) -{ 1 }-> 1 + choice(clause) + guess(cnf) :|: cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.62	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.62	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, y'), 2, if(eq(1 + (z - 1), y4), 2, member(1 + (z - 1), ys''))) :|: z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(z - 1, y'), 2, 0) :|: z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, y2), 2, if(eq(1 + (z - 1), y7), 2, member(1 + (z - 1), ys3))) :|: y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.62	   member(z, z') -{ 2 }-> if(eq(z - 1, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(eq(z - 1, z' - 3), 2, 0) :|: z - 1 >= 0, z' - 3 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> if(0, 2, if(eq(z, y8), 2, member(z, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y5), 2, member(1 + (z - 1), ys1))) :|: y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y6), 2, member(1 + (z - 1), ys2))) :|: y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.62	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.62	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.62	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.62	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.62	   sat(z) -{ 2 }-> satck(1 + clause' + cnf', 1 + choice(clause') + guess(cnf')) :|: clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.62	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.62	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.62	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.62	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.62	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.62	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.62	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.62	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.62	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.62	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.62	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.62	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.62	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.62	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.62	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	
380.25/291.62	Function symbols to be analyzed: {choice}, {eq}, {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(19) IntTrsBoundProof (UPPER BOUND(ID))
380.25/291.62	
380.25/291.62	Computed SIZE bound using KoAT for: choice
380.25/291.62	after applying outer abstraction to obtain an ITS,
380.25/291.62	resulting in: O(n^1) with polynomial bound: z
380.25/291.62	
380.25/291.62	----------------------------------------
380.25/291.62	
380.25/291.62	(20)
380.25/291.62	Obligation:
380.25/291.62	Complexity RNTS consisting of the following rules:
380.25/291.62	
380.25/291.62	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 1 }-> choice(xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.62	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.62	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.62	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.62	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.62	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.62	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.62	   guess(z) -{ 1 }-> 1 + choice(clause) + guess(cnf) :|: cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.62	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.62	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.62	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.62	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y'), 2, if(eq(1 + (z - 1), y4), 2, member(1 + (z - 1), ys''))) :|: z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y'), 2, 0) :|: z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y2), 2, if(eq(1 + (z - 1), y7), 2, member(1 + (z - 1), ys3))) :|: y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, z' - 3), 2, 0) :|: z - 1 >= 0, z' - 3 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(0, 2, if(eq(z, y8), 2, member(z, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y5), 2, member(1 + (z - 1), ys1))) :|: y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y6), 2, member(1 + (z - 1), ys2))) :|: y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.63	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.63	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.63	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.63	   sat(z) -{ 2 }-> satck(1 + clause' + cnf', 1 + choice(clause') + guess(cnf')) :|: clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.63	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.63	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.63	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.63	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.63	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.63	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.63	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.63	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.63	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.63	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	
380.25/291.63	Function symbols to be analyzed: {choice}, {eq}, {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.25/291.63	Previous analysis results are:
380.25/291.63	  choice: runtime: ?, size: O(n^1) [z]
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(21) IntTrsBoundProof (UPPER BOUND(ID))
380.25/291.63	
380.25/291.63	Computed RUNTIME bound using KoAT for: choice
380.25/291.63	after applying outer abstraction to obtain an ITS,
380.25/291.63	resulting in: O(n^1) with polynomial bound: 1 + z
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(22)
380.25/291.63	Obligation:
380.25/291.63	Complexity RNTS consisting of the following rules:
380.25/291.63	
380.25/291.63	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 1 }-> choice(xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.63	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.63	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   guess(z) -{ 1 }-> 1 + choice(clause) + guess(cnf) :|: cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.63	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.63	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y'), 2, if(eq(1 + (z - 1), y4), 2, member(1 + (z - 1), ys''))) :|: z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y'), 2, 0) :|: z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y2), 2, if(eq(1 + (z - 1), y7), 2, member(1 + (z - 1), ys3))) :|: y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, z' - 3), 2, 0) :|: z - 1 >= 0, z' - 3 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(0, 2, if(eq(z, y8), 2, member(z, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y5), 2, member(1 + (z - 1), ys1))) :|: y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y6), 2, member(1 + (z - 1), ys2))) :|: y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.63	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.63	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.63	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.63	   sat(z) -{ 2 }-> satck(1 + clause' + cnf', 1 + choice(clause') + guess(cnf')) :|: clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.63	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.63	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.63	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.63	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.63	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.63	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.63	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.63	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.63	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.63	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	
380.25/291.63	Function symbols to be analyzed: {eq}, {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.25/291.63	Previous analysis results are:
380.25/291.63	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(23) ResultPropagationProof (UPPER BOUND(ID))
380.25/291.63	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(24)
380.25/291.63	Obligation:
380.25/291.63	Complexity RNTS consisting of the following rules:
380.25/291.63	
380.25/291.63	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.63	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.63	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.63	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.63	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y'), 2, if(eq(1 + (z - 1), y4), 2, member(1 + (z - 1), ys''))) :|: z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y'), 2, 0) :|: z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y2), 2, if(eq(1 + (z - 1), y7), 2, member(1 + (z - 1), ys3))) :|: y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, z' - 3), 2, 0) :|: z - 1 >= 0, z' - 3 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(0, 2, if(eq(z, y8), 2, member(z, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y5), 2, member(1 + (z - 1), ys1))) :|: y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y6), 2, member(1 + (z - 1), ys2))) :|: y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.63	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.63	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.63	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.63	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.63	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.63	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.63	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.63	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.63	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.63	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.63	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.63	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.63	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.63	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	
380.25/291.63	Function symbols to be analyzed: {eq}, {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.25/291.63	Previous analysis results are:
380.25/291.63	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(25) IntTrsBoundProof (UPPER BOUND(ID))
380.25/291.63	
380.25/291.63	Computed SIZE bound using CoFloCo for: eq
380.25/291.63	after applying outer abstraction to obtain an ITS,
380.25/291.63	resulting in: O(1) with polynomial bound: 2
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(26)
380.25/291.63	Obligation:
380.25/291.63	Complexity RNTS consisting of the following rules:
380.25/291.63	
380.25/291.63	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.63	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.63	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.63	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.63	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y'), 2, if(eq(1 + (z - 1), y4), 2, member(1 + (z - 1), ys''))) :|: z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y'), 2, 0) :|: z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y2), 2, if(eq(1 + (z - 1), y7), 2, member(1 + (z - 1), ys3))) :|: y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, z' - 3), 2, 0) :|: z - 1 >= 0, z' - 3 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(0, 2, if(eq(z, y8), 2, member(z, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y5), 2, member(1 + (z - 1), ys1))) :|: y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y6), 2, member(1 + (z - 1), ys2))) :|: y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.63	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.63	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.63	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.63	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.63	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.63	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.63	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.63	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.63	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.63	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.63	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.63	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.63	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.63	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	
380.25/291.63	Function symbols to be analyzed: {eq}, {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.25/291.63	Previous analysis results are:
380.25/291.63	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.25/291.63	  eq: runtime: ?, size: O(1) [2]
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(27) IntTrsBoundProof (UPPER BOUND(ID))
380.25/291.63	
380.25/291.63	Computed RUNTIME bound using CoFloCo for: eq
380.25/291.63	after applying outer abstraction to obtain an ITS,
380.25/291.63	resulting in: O(n^1) with polynomial bound: 2 + z'
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(28)
380.25/291.63	Obligation:
380.25/291.63	Complexity RNTS consisting of the following rules:
380.25/291.63	
380.25/291.63	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> eq(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.63	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.63	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.63	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.63	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y'), 2, if(eq(1 + (z - 1), y4), 2, member(1 + (z - 1), ys''))) :|: z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y'), 2, 0) :|: z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, y2), 2, if(eq(1 + (z - 1), y7), 2, member(1 + (z - 1), ys3))) :|: y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.63	   member(z, z') -{ 2 }-> if(eq(z - 1, y2), 2, 0) :|: z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(eq(z - 1, z' - 3), 2, 0) :|: z - 1 >= 0, z' - 3 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(2, 2, if(eq(1, y3), 2, member(1, ys'))) :|: z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> if(0, 2, if(eq(z, y8), 2, member(z, ys4))) :|: z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y5), 2, member(1 + (z - 1), ys1))) :|: y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> if(0, 2, if(eq(1 + (z - 1), y6), 2, member(1 + (z - 1), ys2))) :|: y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.63	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.63	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.63	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.63	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.63	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.63	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.63	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.63	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.63	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.63	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.63	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.63	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.63	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.63	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	
380.25/291.63	Function symbols to be analyzed: {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.25/291.63	Previous analysis results are:
380.25/291.63	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.25/291.63	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(29) ResultPropagationProof (UPPER BOUND(ID))
380.25/291.63	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(30)
380.25/291.63	Obligation:
380.25/291.63	Complexity RNTS consisting of the following rules:
380.25/291.63	
380.25/291.63	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.63	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.63	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.63	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.63	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 + y2 }-> if(s11, 2, 0) :|: s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 2 + z' }-> if(s3, 2, 0) :|: s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.25/291.63	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.63	   member(z, z') -{ 4 + y' }-> if(s6, 2, 0) :|: s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.63	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.25/291.63	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.25/291.63	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.25/291.63	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.25/291.63	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.25/291.63	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.25/291.63	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.25/291.63	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.25/291.63	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.25/291.63	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.25/291.63	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.25/291.63	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.25/291.63	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.25/291.63	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.25/291.63	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.25/291.63	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.25/291.63	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.25/291.63	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.25/291.63	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.25/291.63	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.25/291.63	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.25/291.63	   verify(z) -{ 1 }-> 2 :|: z = 1
380.25/291.63	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	
380.25/291.63	Function symbols to be analyzed: {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.25/291.63	Previous analysis results are:
380.25/291.63	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.25/291.63	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(31) IntTrsBoundProof (UPPER BOUND(ID))
380.25/291.63	
380.25/291.63	Computed SIZE bound using CoFloCo for: negate
380.25/291.63	after applying outer abstraction to obtain an ITS,
380.25/291.63	resulting in: O(n^1) with polynomial bound: z
380.25/291.63	
380.25/291.63	----------------------------------------
380.25/291.63	
380.25/291.63	(32)
380.25/291.63	Obligation:
380.25/291.63	Complexity RNTS consisting of the following rules:
380.25/291.63	
380.25/291.63	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.25/291.63	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.25/291.63	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.25/291.63	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.25/291.63	   guess(z) -{ 1 }-> 1 :|: z = 1
380.25/291.63	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.25/291.63	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.25/291.63	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.25/291.63	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.25/291.63	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.25/291.63	   member(z, z') -{ 4 + y2 }-> if(s11, 2, 0) :|: s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.25/291.63	   member(z, z') -{ 2 + z' }-> if(s3, 2, 0) :|: s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.25/291.63	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.25/291.63	   member(z, z') -{ 4 + y' }-> if(s6, 2, 0) :|: s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.25/291.63	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.64	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.64	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.64	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.64	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.64	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.64	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.64	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.64	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.64	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.64	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.64	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.64	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.64	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.64	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.64	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.64	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.64	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.64	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.64	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.64	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.64	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.64	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.64	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.64	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.64	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.64	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.64	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.64	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.64	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.64	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.64	
380.41/291.64	Function symbols to be analyzed: {negate}, {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.41/291.64	Previous analysis results are:
380.41/291.64	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.64	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.64	  negate: runtime: ?, size: O(n^1) [z]
380.41/291.64	
380.41/291.64	----------------------------------------
380.41/291.64	
380.41/291.64	(33) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.64	
380.41/291.64	Computed RUNTIME bound using CoFloCo for: negate
380.41/291.64	after applying outer abstraction to obtain an ITS,
380.41/291.64	resulting in: O(1) with polynomial bound: 1
380.41/291.64	
380.41/291.64	----------------------------------------
380.41/291.64	
380.41/291.64	(34)
380.41/291.64	Obligation:
380.41/291.64	Complexity RNTS consisting of the following rules:
380.41/291.64	
380.41/291.64	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.64	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.64	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.64	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.64	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.64	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.64	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.64	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.64	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.64	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.64	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.64	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.64	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.64	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.64	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.64	   member(z, z') -{ 4 + y2 }-> if(s11, 2, 0) :|: s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.64	   member(z, z') -{ 2 + z' }-> if(s3, 2, 0) :|: s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.64	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.64	   member(z, z') -{ 4 + y' }-> if(s6, 2, 0) :|: s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.64	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.64	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.64	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.64	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.64	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.64	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.64	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.64	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.64	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.64	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.64	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.64	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.64	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.64	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.64	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.64	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.64	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.64	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.64	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.64	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.64	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.64	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.64	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.64	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.64	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.64	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.64	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.64	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.64	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.64	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.64	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.64	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.64	
380.41/291.64	Function symbols to be analyzed: {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.41/291.64	Previous analysis results are:
380.41/291.64	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.64	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.64	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.64	
380.41/291.64	----------------------------------------
380.41/291.64	
380.41/291.64	(35) ResultPropagationProof (UPPER BOUND(ID))
380.41/291.64	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.41/291.64	----------------------------------------
380.41/291.64	
380.41/291.64	(36)
380.41/291.64	Obligation:
380.41/291.64	Complexity RNTS consisting of the following rules:
380.41/291.64	
380.41/291.64	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.64	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.64	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.64	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.64	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.64	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.64	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.64	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.64	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.64	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.64	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.64	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.64	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.64	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.64	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.64	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.64	   member(z, z') -{ 4 + y2 }-> if(s11, 2, 0) :|: s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.64	   member(z, z') -{ 2 + z' }-> if(s3, 2, 0) :|: s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.64	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 4 + y' }-> if(s6, 2, 0) :|: s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(37) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed SIZE bound using CoFloCo for: if
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(n^1) with polynomial bound: z' + z''
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(38)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 4 + y2 }-> if(s11, 2, 0) :|: s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 2 + z' }-> if(s3, 2, 0) :|: s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 4 + y' }-> if(s6, 2, 0) :|: s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {if}, {guess}, {member}, {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: ?, size: O(n^1) [z' + z'']
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(39) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed RUNTIME bound using CoFloCo for: if
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(1) with polynomial bound: 1
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(40)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 4 + y2 }-> if(s11, 2, 0) :|: s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 2 + z' }-> if(s3, 2, 0) :|: s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 4 + y' }-> if(s6, 2, 0) :|: s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {guess}, {member}, {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(41) ResultPropagationProof (UPPER BOUND(ID))
380.41/291.65	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(42)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {guess}, {member}, {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(43) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed SIZE bound using KoAT for: guess
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(n^1) with polynomial bound: z
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(44)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {guess}, {member}, {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: ?, size: O(n^1) [z]
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(45) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed RUNTIME bound using CoFloCo for: guess
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(n^1) with polynomial bound: 3 + 2*z
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(46)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 2 + clause }-> 1 + s' + guess(cnf) :|: s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 3 + clause' }-> satck(1 + clause' + cnf', 1 + s'' + guess(cnf')) :|: s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {member}, {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(47) ResultPropagationProof (UPPER BOUND(ID))
380.41/291.65	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(48)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {member}, {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(49) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed SIZE bound using KoAT for: member
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(n^1) with polynomial bound: 2*z'
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(50)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {member}, {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	  member: runtime: ?, size: O(n^1) [2*z']
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(51) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed RUNTIME bound using CoFloCo for: member
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(n^1) with polynomial bound: 39 + 27*z'
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(52)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 7 + y' + y4 }-> if(s4, 2, if(s5, 2, member(1 + (z - 1), ys''))) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 7 + y2 + y7 }-> if(s9, 2, if(s10, 2, member(1 + (z - 1), ys3))) :|: s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 5 + y3 }-> if(2, 2, if(s2, 2, member(1, ys'))) :|: s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 4 + y8 }-> if(0, 2, if(s12, 2, member(z, ys4))) :|: s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 5 + y5 }-> if(0, 2, if(s7, 2, member(1 + (z - 1), ys1))) :|: s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 5 + y6 }-> if(0, 2, if(s8, 2, member(1 + (z - 1), ys2))) :|: s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> if(if(member(0, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 3 }-> if(if(member(1 + x, ls2), 0, verify(ls2)), 1 + l2 + ls2, 3) :|: z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 1 }-> if(member(0, ls), 0, 0) :|: l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1), 0, 2) :|: z - 2 >= 0
380.41/291.65	   verify(z) -{ 2 }-> if(member(0, 1 + l1 + ls1), 0, if(member(0, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 3 }-> if(member(0, 1 + l1 + ls1), 0, if(member(1 + x, ls1), 0, verify(ls1))) :|: z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x3, ls), 0, 0) :|: z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(0, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x3, 1 + l' + ls'), 0, if(member(1 + x, ls'), 0, verify(ls'))) :|: ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 2 }-> if(member(1 + x4, ls), 0, 0) :|: x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(0, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 4 }-> if(member(1 + x4, 1 + l'' + ls''), 0, if(member(1 + x, ls''), 0, verify(ls''))) :|: x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 3 }-> if(member(1 + (z - 3), 1), 0, 2) :|: z - 3 >= 0
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(53) ResultPropagationProof (UPPER BOUND(ID))
380.41/291.65	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(54)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 41 + 27*ls2 }-> if(if(s58, 0, verify(ls2)), 1 + l2 + ls2, 3) :|: s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 42 + 27*ls2 }-> if(if(s59, 0, verify(ls2)), 1 + l2 + ls2, 3) :|: s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.65	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 108 + 27*l' + 54*ls' }-> if(s46, 0, if(s47, 0, verify(ls'))) :|: s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 109 + 27*l' + 54*ls' }-> if(s48, 0, if(s49, 0, verify(ls'))) :|: s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 108 + 27*l'' + 54*ls'' }-> if(s50, 0, if(s51, 0, verify(ls''))) :|: s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 109 + 27*l'' + 54*ls'' }-> if(s52, 0, if(s53, 0, verify(ls''))) :|: s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 107 + 27*l1 + 54*ls1 }-> if(s54, 0, if(s55, 0, verify(ls1))) :|: s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 108 + 27*l1 + 54*ls1 }-> if(s56, 0, if(s57, 0, verify(ls1))) :|: s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(55) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed SIZE bound using CoFloCo for: verify
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(1) with polynomial bound: 2
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(56)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 41 + 27*ls2 }-> if(if(s58, 0, verify(ls2)), 1 + l2 + ls2, 3) :|: s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 42 + 27*ls2 }-> if(if(s59, 0, verify(ls2)), 1 + l2 + ls2, 3) :|: s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.65	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 108 + 27*l' + 54*ls' }-> if(s46, 0, if(s47, 0, verify(ls'))) :|: s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 109 + 27*l' + 54*ls' }-> if(s48, 0, if(s49, 0, verify(ls'))) :|: s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 108 + 27*l'' + 54*ls'' }-> if(s50, 0, if(s51, 0, verify(ls''))) :|: s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 109 + 27*l'' + 54*ls'' }-> if(s52, 0, if(s53, 0, verify(ls''))) :|: s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 107 + 27*l1 + 54*ls1 }-> if(s54, 0, if(s55, 0, verify(ls1))) :|: s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 108 + 27*l1 + 54*ls1 }-> if(s56, 0, if(s57, 0, verify(ls1))) :|: s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {verify}, {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.65	  verify: runtime: ?, size: O(1) [2]
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(57) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed RUNTIME bound using CoFloCo for: verify
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(n^2) with polynomial bound: 617 + 505*z + 108*z^2
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(58)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 41 + 27*ls2 }-> if(if(s58, 0, verify(ls2)), 1 + l2 + ls2, 3) :|: s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 42 + 27*ls2 }-> if(if(s59, 0, verify(ls2)), 1 + l2 + ls2, 3) :|: s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.65	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 108 + 27*l' + 54*ls' }-> if(s46, 0, if(s47, 0, verify(ls'))) :|: s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 109 + 27*l' + 54*ls' }-> if(s48, 0, if(s49, 0, verify(ls'))) :|: s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 108 + 27*l'' + 54*ls'' }-> if(s50, 0, if(s51, 0, verify(ls''))) :|: s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 109 + 27*l'' + 54*ls'' }-> if(s52, 0, if(s53, 0, verify(ls''))) :|: s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 107 + 27*l1 + 54*ls1 }-> if(s54, 0, if(s55, 0, verify(ls1))) :|: s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 108 + 27*l1 + 54*ls1 }-> if(s56, 0, if(s57, 0, verify(ls1))) :|: s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.65	  verify: runtime: O(n^2) [617 + 505*z + 108*z^2], size: O(1) [2]
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(59) ResultPropagationProof (UPPER BOUND(ID))
380.41/291.65	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(60)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 660 + 532*ls2 + 108*ls2^2 }-> s80 :|: s78 >= 0, s78 <= 2, s79 >= 0, s79 <= s78 + 0, s80 >= 0, s80 <= 3 + (1 + l2 + ls2), s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 661 + 532*ls2 + 108*ls2^2 }-> s83 :|: s81 >= 0, s81 <= 2, s82 >= 0, s82 <= s81 + 0, s83 >= 0, s83 <= 3 + (1 + l2 + ls2), s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.65	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 727 + 27*l' + 559*ls' + 108*ls'^2 }-> s62 :|: s60 >= 0, s60 <= 2, s61 >= 0, s61 <= s60 + 0, s62 >= 0, s62 <= s61 + 0, s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 728 + 27*l' + 559*ls' + 108*ls'^2 }-> s65 :|: s63 >= 0, s63 <= 2, s64 >= 0, s64 <= s63 + 0, s65 >= 0, s65 <= s64 + 0, s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 727 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s68 :|: s66 >= 0, s66 <= 2, s67 >= 0, s67 <= s66 + 0, s68 >= 0, s68 <= s67 + 0, s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 728 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s71 :|: s69 >= 0, s69 <= 2, s70 >= 0, s70 <= s69 + 0, s71 >= 0, s71 <= s70 + 0, s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 726 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s74 :|: s72 >= 0, s72 <= 2, s73 >= 0, s73 <= s72 + 0, s74 >= 0, s74 <= s73 + 0, s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 727 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s77 :|: s75 >= 0, s75 <= 2, s76 >= 0, s76 <= s75 + 0, s77 >= 0, s77 <= s76 + 0, s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.65	  verify: runtime: O(n^2) [617 + 505*z + 108*z^2], size: O(1) [2]
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(61) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed SIZE bound using CoFloCo for: satck
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(n^1) with polynomial bound: 3 + z'
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(62)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 660 + 532*ls2 + 108*ls2^2 }-> s80 :|: s78 >= 0, s78 <= 2, s79 >= 0, s79 <= s78 + 0, s80 >= 0, s80 <= 3 + (1 + l2 + ls2), s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 661 + 532*ls2 + 108*ls2^2 }-> s83 :|: s81 >= 0, s81 <= 2, s82 >= 0, s82 <= s81 + 0, s83 >= 0, s83 <= 3 + (1 + l2 + ls2), s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.65	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 727 + 27*l' + 559*ls' + 108*ls'^2 }-> s62 :|: s60 >= 0, s60 <= 2, s61 >= 0, s61 <= s60 + 0, s62 >= 0, s62 <= s61 + 0, s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 728 + 27*l' + 559*ls' + 108*ls'^2 }-> s65 :|: s63 >= 0, s63 <= 2, s64 >= 0, s64 <= s63 + 0, s65 >= 0, s65 <= s64 + 0, s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 727 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s68 :|: s66 >= 0, s66 <= 2, s67 >= 0, s67 <= s66 + 0, s68 >= 0, s68 <= s67 + 0, s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 728 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s71 :|: s69 >= 0, s69 <= 2, s70 >= 0, s70 <= s69 + 0, s71 >= 0, s71 <= s70 + 0, s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 726 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s74 :|: s72 >= 0, s72 <= 2, s73 >= 0, s73 <= s72 + 0, s74 >= 0, s74 <= s73 + 0, s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 727 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s77 :|: s75 >= 0, s75 <= 2, s76 >= 0, s76 <= s75 + 0, s77 >= 0, s77 <= s76 + 0, s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {satck}, {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.65	  verify: runtime: O(n^2) [617 + 505*z + 108*z^2], size: O(1) [2]
380.41/291.65	  satck: runtime: ?, size: O(n^1) [3 + z']
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(63) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.65	
380.41/291.65	Computed RUNTIME bound using KoAT for: satck
380.41/291.65	after applying outer abstraction to obtain an ITS,
380.41/291.65	resulting in: O(n^2) with polynomial bound: 1329 + 1064*z' + 216*z'^2
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(64)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 1 }-> satck(z, 0) :|: z >= 0
380.41/291.65	   sat(z) -{ 2 }-> satck(1, 1) :|: z = 1
380.41/291.65	   sat(z) -{ 6 + clause' + 2*cnf' }-> satck(1 + clause' + cnf', 1 + s'' + s17) :|: s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 660 + 532*ls2 + 108*ls2^2 }-> s80 :|: s78 >= 0, s78 <= 2, s79 >= 0, s79 <= s78 + 0, s80 >= 0, s80 <= 3 + (1 + l2 + ls2), s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 661 + 532*ls2 + 108*ls2^2 }-> s83 :|: s81 >= 0, s81 <= 2, s82 >= 0, s82 <= s81 + 0, s83 >= 0, s83 <= 3 + (1 + l2 + ls2), s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.65	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 727 + 27*l' + 559*ls' + 108*ls'^2 }-> s62 :|: s60 >= 0, s60 <= 2, s61 >= 0, s61 <= s60 + 0, s62 >= 0, s62 <= s61 + 0, s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 728 + 27*l' + 559*ls' + 108*ls'^2 }-> s65 :|: s63 >= 0, s63 <= 2, s64 >= 0, s64 <= s63 + 0, s65 >= 0, s65 <= s64 + 0, s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 727 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s68 :|: s66 >= 0, s66 <= 2, s67 >= 0, s67 <= s66 + 0, s68 >= 0, s68 <= s67 + 0, s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 728 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s71 :|: s69 >= 0, s69 <= 2, s70 >= 0, s70 <= s69 + 0, s71 >= 0, s71 <= s70 + 0, s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 726 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s74 :|: s72 >= 0, s72 <= 2, s73 >= 0, s73 <= s72 + 0, s74 >= 0, s74 <= s73 + 0, s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 727 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s77 :|: s75 >= 0, s75 <= 2, s76 >= 0, s76 <= s75 + 0, s77 >= 0, s77 <= s76 + 0, s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.65	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.65	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.65	  verify: runtime: O(n^2) [617 + 505*z + 108*z^2], size: O(1) [2]
380.41/291.65	  satck: runtime: O(n^2) [1329 + 1064*z' + 216*z'^2], size: O(n^1) [3 + z']
380.41/291.65	
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(65) ResultPropagationProof (UPPER BOUND(ID))
380.41/291.65	Applied inner abstraction using the recently inferred runtime/size bounds where possible.
380.41/291.65	----------------------------------------
380.41/291.65	
380.41/291.65	(66)
380.41/291.65	Obligation:
380.41/291.65	Complexity RNTS consisting of the following rules:
380.41/291.65	
380.41/291.65	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.65	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.65	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.65	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.65	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.65	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.65	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.65	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.65	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.65	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.65	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.65	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.65	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.65	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.65	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.65	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.65	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.65	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.65	   sat(z) -{ 2611 }-> s84 :|: s84 >= 0, s84 <= 1 + 3, z = 1
380.41/291.65	   sat(z) -{ 2615 + clause' + 2*cnf' + 1496*s'' + 432*s''*s17 + 216*s''^2 + 1496*s17 + 216*s17^2 }-> s85 :|: s85 >= 0, s85 <= 1 + s'' + s17 + 3, s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.65	   sat(z) -{ 1330 }-> s86 :|: s86 >= 0, s86 <= 0 + 3, z >= 0
380.41/291.65	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.65	   satck(z, z') -{ 660 + 532*ls2 + 108*ls2^2 }-> s80 :|: s78 >= 0, s78 <= 2, s79 >= 0, s79 <= s78 + 0, s80 >= 0, s80 <= 3 + (1 + l2 + ls2), s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.65	   satck(z, z') -{ 661 + 532*ls2 + 108*ls2^2 }-> s83 :|: s81 >= 0, s81 <= 2, s82 >= 0, s82 <= s81 + 0, s83 >= 0, s83 <= 3 + (1 + l2 + ls2), s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.65	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.65	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.65	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.65	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.65	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.65	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.65	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.65	   verify(z) -{ 727 + 27*l' + 559*ls' + 108*ls'^2 }-> s62 :|: s60 >= 0, s60 <= 2, s61 >= 0, s61 <= s60 + 0, s62 >= 0, s62 <= s61 + 0, s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.65	   verify(z) -{ 728 + 27*l' + 559*ls' + 108*ls'^2 }-> s65 :|: s63 >= 0, s63 <= 2, s64 >= 0, s64 <= s63 + 0, s65 >= 0, s65 <= s64 + 0, s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.65	   verify(z) -{ 727 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s68 :|: s66 >= 0, s66 <= 2, s67 >= 0, s67 <= s66 + 0, s68 >= 0, s68 <= s67 + 0, s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.65	   verify(z) -{ 728 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s71 :|: s69 >= 0, s69 <= 2, s70 >= 0, s70 <= s69 + 0, s71 >= 0, s71 <= s70 + 0, s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.65	   verify(z) -{ 726 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s74 :|: s72 >= 0, s72 <= 2, s73 >= 0, s73 <= s72 + 0, s74 >= 0, s74 <= s73 + 0, s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.65	   verify(z) -{ 727 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s77 :|: s75 >= 0, s75 <= 2, s76 >= 0, s76 <= s75 + 0, s77 >= 0, s77 <= s76 + 0, s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.65	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.65	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.65	
380.41/291.65	Function symbols to be analyzed: {sat}
380.41/291.65	Previous analysis results are:
380.41/291.65	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.65	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.65	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.65	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.66	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.66	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.66	  verify: runtime: O(n^2) [617 + 505*z + 108*z^2], size: O(1) [2]
380.41/291.66	  satck: runtime: O(n^2) [1329 + 1064*z' + 216*z'^2], size: O(n^1) [3 + z']
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(67) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.66	
380.41/291.66	Computed SIZE bound using CoFloCo for: sat
380.41/291.66	after applying outer abstraction to obtain an ITS,
380.41/291.66	resulting in: O(n^1) with polynomial bound: 3 + z
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(68)
380.41/291.66	Obligation:
380.41/291.66	Complexity RNTS consisting of the following rules:
380.41/291.66	
380.41/291.66	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.66	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.66	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.66	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.66	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.66	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.66	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.66	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.66	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.66	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.66	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.66	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.66	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.66	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.66	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.66	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.66	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.66	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.66	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.66	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.66	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.66	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.66	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.66	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.66	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.66	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.66	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.66	   sat(z) -{ 2611 }-> s84 :|: s84 >= 0, s84 <= 1 + 3, z = 1
380.41/291.66	   sat(z) -{ 2615 + clause' + 2*cnf' + 1496*s'' + 432*s''*s17 + 216*s''^2 + 1496*s17 + 216*s17^2 }-> s85 :|: s85 >= 0, s85 <= 1 + s'' + s17 + 3, s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.66	   sat(z) -{ 1330 }-> s86 :|: s86 >= 0, s86 <= 0 + 3, z >= 0
380.41/291.66	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.66	   satck(z, z') -{ 660 + 532*ls2 + 108*ls2^2 }-> s80 :|: s78 >= 0, s78 <= 2, s79 >= 0, s79 <= s78 + 0, s80 >= 0, s80 <= 3 + (1 + l2 + ls2), s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.66	   satck(z, z') -{ 661 + 532*ls2 + 108*ls2^2 }-> s83 :|: s81 >= 0, s81 <= 2, s82 >= 0, s82 <= s81 + 0, s83 >= 0, s83 <= 3 + (1 + l2 + ls2), s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.66	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.66	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.66	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.66	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.66	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.66	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.66	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.66	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.66	   verify(z) -{ 727 + 27*l' + 559*ls' + 108*ls'^2 }-> s62 :|: s60 >= 0, s60 <= 2, s61 >= 0, s61 <= s60 + 0, s62 >= 0, s62 <= s61 + 0, s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.66	   verify(z) -{ 728 + 27*l' + 559*ls' + 108*ls'^2 }-> s65 :|: s63 >= 0, s63 <= 2, s64 >= 0, s64 <= s63 + 0, s65 >= 0, s65 <= s64 + 0, s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.66	   verify(z) -{ 727 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s68 :|: s66 >= 0, s66 <= 2, s67 >= 0, s67 <= s66 + 0, s68 >= 0, s68 <= s67 + 0, s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.66	   verify(z) -{ 728 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s71 :|: s69 >= 0, s69 <= 2, s70 >= 0, s70 <= s69 + 0, s71 >= 0, s71 <= s70 + 0, s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.66	   verify(z) -{ 726 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s74 :|: s72 >= 0, s72 <= 2, s73 >= 0, s73 <= s72 + 0, s74 >= 0, s74 <= s73 + 0, s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.66	   verify(z) -{ 727 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s77 :|: s75 >= 0, s75 <= 2, s76 >= 0, s76 <= s75 + 0, s77 >= 0, s77 <= s76 + 0, s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.66	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.66	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.66	
380.41/291.66	Function symbols to be analyzed: {sat}
380.41/291.66	Previous analysis results are:
380.41/291.66	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.66	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.66	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.66	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.66	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.66	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.66	  verify: runtime: O(n^2) [617 + 505*z + 108*z^2], size: O(1) [2]
380.41/291.66	  satck: runtime: O(n^2) [1329 + 1064*z' + 216*z'^2], size: O(n^1) [3 + z']
380.41/291.66	  sat: runtime: ?, size: O(n^1) [3 + z]
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(69) IntTrsBoundProof (UPPER BOUND(ID))
380.41/291.66	
380.41/291.66	Computed RUNTIME bound using KoAT for: sat
380.41/291.66	after applying outer abstraction to obtain an ITS,
380.41/291.66	resulting in: O(n^2) with polynomial bound: 6556 + 2995*z + 864*z^2
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(70)
380.41/291.66	Obligation:
380.41/291.66	Complexity RNTS consisting of the following rules:
380.41/291.66	
380.41/291.66	   choice(z) -{ 2 + xs }-> s :|: s >= 0, s <= xs, z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.66	   choice(z) -{ 1 }-> x :|: z = 1 + x + xs, xs >= 0, x >= 0
380.41/291.66	   choice(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.66	   eq(z, z') -{ 2 + z' }-> s1 :|: s1 >= 0, s1 <= 2, z - 1 >= 0, z' - 1 >= 0
380.41/291.66	   eq(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1
380.41/291.66	   eq(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0
380.41/291.66	   eq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.66	   guess(z) -{ 1 }-> 1 :|: z = 1
380.41/291.66	   guess(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.66	   guess(z) -{ 5 + clause + 2*cnf }-> 1 + s' + s16 :|: s16 >= 0, s16 <= cnf, s' >= 0, s' <= clause, cnf >= 0, z = 1 + clause + cnf, clause >= 0
380.41/291.66	   if(z, z', z'') -{ 1 }-> z' :|: z = 2, z' >= 0, z'' >= 0
380.41/291.66	   if(z, z', z'') -{ 1 }-> z'' :|: z' >= 0, z'' >= 0, z = 0
380.41/291.66	   if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
380.41/291.66	   member(z, z') -{ 4 }-> e :|: z' - 3 >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 }-> e :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 }-> e :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 }-> e :|: z >= 0, z' - 2 >= 0, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 2 }-> e :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, 2 = t, t >= 0, e >= 0, 0 = 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 + z' }-> s13 :|: s13 >= 0, s13 <= 0 + 2, s3 >= 0, s3 <= 2, z - 1 >= 0, z' - 3 >= 0
380.41/291.66	   member(z, z') -{ 5 + y' }-> s14 :|: s14 >= 0, s14 <= 0 + 2, s6 >= 0, s6 <= 2, z' = 1 + (1 + y') + ys, ys >= 0, z - 1 >= 0, y' >= 0
380.41/291.66	   member(z, z') -{ 5 + y2 }-> s15 :|: s15 >= 0, s15 <= 0 + 2, s11 >= 0, s11 <= 2, z' = 1 + (1 + y2) + ys, ys >= 0, y2 >= 0, z - 1 >= 0
380.41/291.66	   member(z, z') -{ 46 + y3 + 27*ys' }-> s20 :|: s18 >= 0, s18 <= 2 * ys', s19 >= 0, s19 <= s18 + 2, s20 >= 0, s20 <= s19 + 2, s2 >= 0, s2 <= 2, z = 1, ys' >= 0, z' = 1 + 1 + (1 + y3 + ys'), y3 >= 0
380.41/291.66	   member(z, z') -{ 48 + y' + y4 + 27*ys'' }-> s23 :|: s21 >= 0, s21 <= 2 * ys'', s22 >= 0, s22 <= s21 + 2, s23 >= 0, s23 <= s22 + 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z' = 1 + (1 + y') + (1 + y4 + ys''), z - 1 >= 0, y' >= 0, ys'' >= 0, y4 >= 0
380.41/291.66	   member(z, z') -{ 46 + y5 + 27*ys1 }-> s26 :|: s24 >= 0, s24 <= 2 * ys1, s25 >= 0, s25 <= s24 + 2, s26 >= 0, s26 <= s25 + 2, s7 >= 0, s7 <= 2, y5 >= 0, ys1 >= 0, z' = 1 + (1 + y'') + (1 + y5 + ys1), y'' >= 0, z - 1 >= 0
380.41/291.66	   member(z, z') -{ 46 + y6 + 27*ys2 }-> s29 :|: s27 >= 0, s27 <= 2 * ys2, s28 >= 0, s28 <= s27 + 2, s29 >= 0, s29 <= s28 + 2, s8 >= 0, s8 <= 2, y1 >= 0, z - 1 >= 0, z' = 1 + (1 + y1) + (1 + y6 + ys2), y6 >= 0, ys2 >= 0
380.41/291.66	   member(z, z') -{ 48 + y2 + y7 + 27*ys3 }-> s32 :|: s30 >= 0, s30 <= 2 * ys3, s31 >= 0, s31 <= s30 + 2, s32 >= 0, s32 <= s31 + 2, s9 >= 0, s9 <= 2, s10 >= 0, s10 <= 2, y7 >= 0, ys3 >= 0, y2 >= 0, z - 1 >= 0, z' = 1 + (1 + y2) + (1 + y7 + ys3)
380.41/291.66	   member(z, z') -{ 45 + y8 + 27*ys4 }-> s35 :|: s33 >= 0, s33 <= 2 * ys4, s34 >= 0, s34 <= s33 + 2, s35 >= 0, s35 <= s34 + 2, s12 >= 0, s12 <= 2, z' = 1 + y + (1 + y8 + ys4), y8 >= 0, z >= 0, y >= 0, ys4 >= 0
380.41/291.66	   member(z, z') -{ 4 }-> t :|: z' = 1 + 1 + 1, z = 1, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.66	   member(z, z') -{ 3 }-> t :|: z = 1, z' - 2 >= 0, 2 = 2, 2 = t, t >= 0, e >= 0, 0 = e
380.41/291.66	   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 1
380.41/291.66	   member(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
380.41/291.66	   member(z, z') -{ 3 }-> 0 :|: z' = 1 + 1 + 1, z = 1, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 2 }-> 0 :|: z = 1, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 2 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 3 }-> 0 :|: z' - 3 >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 2 }-> 0 :|: z' = 1 + (1 + y'') + ys, ys >= 0, y'' >= 0, z - 1 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 2 }-> 0 :|: y1 >= 0, z - 1 >= 0, ys >= 0, z' = 1 + (1 + y1) + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 2 }-> 0 :|: z >= 0, z' - 2 >= 0, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   member(z, z') -{ 1 }-> 0 :|: ys >= 0, z >= 0, y >= 0, z' = 1 + y + ys, v0 >= 0, 0 = v2, v1 >= 0, 0 = v0, 2 = v1, v2 >= 0
380.41/291.66	   negate(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.66	   negate(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
380.41/291.66	   sat(z) -{ 2611 }-> s84 :|: s84 >= 0, s84 <= 1 + 3, z = 1
380.41/291.66	   sat(z) -{ 2615 + clause' + 2*cnf' + 1496*s'' + 432*s''*s17 + 216*s''^2 + 1496*s17 + 216*s17^2 }-> s85 :|: s85 >= 0, s85 <= 1 + s'' + s17 + 3, s17 >= 0, s17 <= cnf', s'' >= 0, s'' <= clause', clause' >= 0, z = 1 + clause' + cnf', cnf' >= 0
380.41/291.66	   sat(z) -{ 1330 }-> s86 :|: s86 >= 0, s86 <= 0 + 3, z >= 0
380.41/291.66	   satck(z, z') -{ 2 }-> e :|: z >= 0, z' >= 0, e >= 0, 0 = 0, 3 = e
380.41/291.66	   satck(z, z') -{ 660 + 532*ls2 + 108*ls2^2 }-> s80 :|: s78 >= 0, s78 <= 2, s79 >= 0, s79 <= s78 + 0, s80 >= 0, s80 <= 3 + (1 + l2 + ls2), s58 >= 0, s58 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, v0 >= 0, l2 = v0
380.41/291.66	   satck(z, z') -{ 661 + 532*ls2 + 108*ls2^2 }-> s83 :|: s81 >= 0, s81 <= 2, s82 >= 0, s82 <= s81 + 0, s83 >= 0, s83 <= 3 + (1 + l2 + ls2), s59 >= 0, s59 <= 2 * ls2, z' = 1 + l2 + ls2, z >= 0, l2 >= 0, ls2 >= 0, x >= 0, l2 = 1 + x
380.41/291.66	   satck(z, z') -{ 3 }-> t :|: z >= 0, z' = 1, 2 = 2, 1 = t, t >= 0, e >= 0, 3 = e
380.41/291.66	   satck(z, z') -{ 2 }-> 0 :|: z >= 0, z' = 1, v0 >= 0, 3 = v2, v1 >= 0, 2 = v0, 1 = v1, v2 >= 0
380.41/291.66	   satck(z, z') -{ 1 }-> 0 :|: z >= 0, z' >= 0, v0 >= 0, 3 = v2, 0 = v0, v2 >= 0
380.41/291.66	   verify(z) -{ 70 }-> s37 :|: s36 >= 0, s36 <= 2 * 1, s37 >= 0, s37 <= 2 + 0, z - 3 >= 0
380.41/291.66	   verify(z) -{ 42 + 27*ls }-> s39 :|: s38 >= 0, s38 <= 2 * ls, s39 >= 0, s39 <= 0 + 0, z = 1 + (1 + x3) + ls, ls >= 0, x3 >= 0
380.41/291.66	   verify(z) -{ 42 + 27*ls }-> s41 :|: s40 >= 0, s40 <= 2 * ls, s41 >= 0, s41 <= 0 + 0, x4 >= 0, ls >= 0, z = 1 + (1 + x4) + ls
380.41/291.66	   verify(z) -{ 69 }-> s43 :|: s42 >= 0, s42 <= 2 * 1, s43 >= 0, s43 <= 2 + 0, z - 2 >= 0
380.41/291.66	   verify(z) -{ 41 + 27*ls }-> s45 :|: s44 >= 0, s44 <= 2 * ls, s45 >= 0, s45 <= 0 + 0, l >= 0, ls >= 0, z = 1 + l + ls
380.41/291.66	   verify(z) -{ 727 + 27*l' + 559*ls' + 108*ls'^2 }-> s62 :|: s60 >= 0, s60 <= 2, s61 >= 0, s61 <= s60 + 0, s62 >= 0, s62 <= s61 + 0, s46 >= 0, s46 <= 2 * (1 + l' + ls'), s47 >= 0, s47 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, v0 >= 0, l' = v0
380.41/291.66	   verify(z) -{ 728 + 27*l' + 559*ls' + 108*ls'^2 }-> s65 :|: s63 >= 0, s63 <= 2, s64 >= 0, s64 <= s63 + 0, s65 >= 0, s65 <= s64 + 0, s48 >= 0, s48 <= 2 * (1 + l' + ls'), s49 >= 0, s49 <= 2 * ls', ls' >= 0, l' >= 0, z = 1 + (1 + x3) + (1 + l' + ls'), x3 >= 0, x >= 0, l' = 1 + x
380.41/291.66	   verify(z) -{ 727 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s68 :|: s66 >= 0, s66 <= 2, s67 >= 0, s67 <= s66 + 0, s68 >= 0, s68 <= s67 + 0, s50 >= 0, s50 <= 2 * (1 + l'' + ls''), s51 >= 0, s51 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, v0 >= 0, l'' = v0
380.41/291.66	   verify(z) -{ 728 + 27*l'' + 559*ls'' + 108*ls''^2 }-> s71 :|: s69 >= 0, s69 <= 2, s70 >= 0, s70 <= s69 + 0, s71 >= 0, s71 <= s70 + 0, s52 >= 0, s52 <= 2 * (1 + l'' + ls''), s53 >= 0, s53 <= 2 * ls'', x4 >= 0, l'' >= 0, z = 1 + (1 + x4) + (1 + l'' + ls''), ls'' >= 0, x >= 0, l'' = 1 + x
380.41/291.66	   verify(z) -{ 726 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s74 :|: s72 >= 0, s72 <= 2, s73 >= 0, s73 <= s72 + 0, s74 >= 0, s74 <= s73 + 0, s54 >= 0, s54 <= 2 * (1 + l1 + ls1), s55 >= 0, s55 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, v0 >= 0, l1 = v0
380.41/291.66	   verify(z) -{ 727 + 27*l1 + 559*ls1 + 108*ls1^2 }-> s77 :|: s75 >= 0, s75 <= 2, s76 >= 0, s76 <= s75 + 0, s77 >= 0, s77 <= s76 + 0, s56 >= 0, s56 <= 2 * (1 + l1 + ls1), s57 >= 0, s57 <= 2 * ls1, z = 1 + l + (1 + l1 + ls1), l >= 0, l1 >= 0, ls1 >= 0, x >= 0, l1 = 1 + x
380.41/291.66	   verify(z) -{ 1 }-> 2 :|: z = 1
380.41/291.66	   verify(z) -{ 0 }-> 0 :|: z >= 0
380.41/291.66	
380.41/291.66	Function symbols to be analyzed: 
380.41/291.66	Previous analysis results are:
380.41/291.66	  choice: runtime: O(n^1) [1 + z], size: O(n^1) [z]
380.41/291.66	  eq: runtime: O(n^1) [2 + z'], size: O(1) [2]
380.41/291.66	  negate: runtime: O(1) [1], size: O(n^1) [z]
380.41/291.66	  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
380.41/291.66	  guess: runtime: O(n^1) [3 + 2*z], size: O(n^1) [z]
380.41/291.66	  member: runtime: O(n^1) [39 + 27*z'], size: O(n^1) [2*z']
380.41/291.66	  verify: runtime: O(n^2) [617 + 505*z + 108*z^2], size: O(1) [2]
380.41/291.66	  satck: runtime: O(n^2) [1329 + 1064*z' + 216*z'^2], size: O(n^1) [3 + z']
380.41/291.66	  sat: runtime: O(n^2) [6556 + 2995*z + 864*z^2], size: O(n^1) [3 + z]
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(71) FinalProof (FINISHED)
380.41/291.66	Computed overall runtime complexity
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(72)
380.41/291.66	BOUNDS(1, n^2)
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(73) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
380.41/291.66	Transformed a relative TRS into a decreasing-loop problem.
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(74)
380.41/291.66	Obligation:
380.41/291.66	Analyzing the following TRS for decreasing loops:
380.41/291.66	
380.41/291.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
380.41/291.66	
380.41/291.66	
380.41/291.66	The TRS R consists of the following rules:
380.41/291.66	
380.41/291.66	   if(true, t, e) -> t
380.41/291.66	   if(false, t, e) -> e
380.41/291.66	   member(x, nil) -> false
380.41/291.66	   member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys))
380.41/291.66	   eq(nil, nil) -> true
380.41/291.66	   eq(O(x), 0(y)) -> eq(x, y)
380.41/291.66	   eq(0(x), 1(y)) -> false
380.41/291.66	   eq(1(x), 0(y)) -> false
380.41/291.66	   eq(1(x), 1(y)) -> eq(x, y)
380.41/291.66	   negate(0(x)) -> 1(x)
380.41/291.66	   negate(1(x)) -> 0(x)
380.41/291.66	   choice(cons(x, xs)) -> x
380.41/291.66	   choice(cons(x, xs)) -> choice(xs)
380.41/291.66	   guess(nil) -> nil
380.41/291.66	   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf))
380.41/291.66	   verify(nil) -> true
380.41/291.66	   verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls))
380.41/291.66	   sat(cnf) -> satck(cnf, guess(cnf))
380.41/291.66	   satck(cnf, assign) -> if(verify(assign), assign, unsat)
380.41/291.66	
380.41/291.66	S is empty.
380.41/291.66	Rewrite Strategy: INNERMOST
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(75) DecreasingLoopProof (LOWER BOUND(ID))
380.41/291.66	The following loop(s) give(s) rise to the lower bound Omega(n^1):
380.41/291.66	
380.41/291.66	The rewrite sequence
380.41/291.66	
380.41/291.66	member(x, cons(y, ys)) ->^+ if(eq(x, y), true, member(x, ys))
380.41/291.66	
380.41/291.66	gives rise to a decreasing loop by considering the right hand sides subterm at position [2].
380.41/291.66	
380.41/291.66	The pumping substitution is [ys / cons(y, ys)].
380.41/291.66	
380.41/291.66	The result substitution is [ ].
380.41/291.66	
380.41/291.66	
380.41/291.66	
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(76)
380.41/291.66	Complex Obligation (BEST)
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(77)
380.41/291.66	Obligation:
380.41/291.66	Proved the lower bound n^1 for the following obligation:
380.41/291.66	
380.41/291.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
380.41/291.66	
380.41/291.66	
380.41/291.66	The TRS R consists of the following rules:
380.41/291.66	
380.41/291.66	   if(true, t, e) -> t
380.41/291.66	   if(false, t, e) -> e
380.41/291.66	   member(x, nil) -> false
380.41/291.66	   member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys))
380.41/291.66	   eq(nil, nil) -> true
380.41/291.66	   eq(O(x), 0(y)) -> eq(x, y)
380.41/291.66	   eq(0(x), 1(y)) -> false
380.41/291.66	   eq(1(x), 0(y)) -> false
380.41/291.66	   eq(1(x), 1(y)) -> eq(x, y)
380.41/291.66	   negate(0(x)) -> 1(x)
380.41/291.66	   negate(1(x)) -> 0(x)
380.41/291.66	   choice(cons(x, xs)) -> x
380.41/291.66	   choice(cons(x, xs)) -> choice(xs)
380.41/291.66	   guess(nil) -> nil
380.41/291.66	   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf))
380.41/291.66	   verify(nil) -> true
380.41/291.66	   verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls))
380.41/291.66	   sat(cnf) -> satck(cnf, guess(cnf))
380.41/291.66	   satck(cnf, assign) -> if(verify(assign), assign, unsat)
380.41/291.66	
380.41/291.66	S is empty.
380.41/291.66	Rewrite Strategy: INNERMOST
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(78) LowerBoundPropagationProof (FINISHED)
380.41/291.66	Propagated lower bound.
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(79)
380.41/291.66	BOUNDS(n^1, INF)
380.41/291.66	
380.41/291.66	----------------------------------------
380.41/291.66	
380.41/291.66	(80)
380.41/291.66	Obligation:
380.41/291.66	Analyzing the following TRS for decreasing loops:
380.41/291.66	
380.41/291.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
380.41/291.66	
380.41/291.66	
380.41/291.66	The TRS R consists of the following rules:
380.41/291.66	
380.41/291.66	   if(true, t, e) -> t
380.41/291.66	   if(false, t, e) -> e
380.41/291.66	   member(x, nil) -> false
380.41/291.66	   member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys))
380.41/291.66	   eq(nil, nil) -> true
380.41/291.66	   eq(O(x), 0(y)) -> eq(x, y)
380.41/291.66	   eq(0(x), 1(y)) -> false
380.41/291.66	   eq(1(x), 0(y)) -> false
380.41/291.66	   eq(1(x), 1(y)) -> eq(x, y)
380.41/291.66	   negate(0(x)) -> 1(x)
380.41/291.66	   negate(1(x)) -> 0(x)
380.41/291.66	   choice(cons(x, xs)) -> x
380.41/291.66	   choice(cons(x, xs)) -> choice(xs)
380.41/291.66	   guess(nil) -> nil
380.41/291.66	   guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf))
380.41/291.66	   verify(nil) -> true
380.41/291.66	   verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls))
380.41/291.66	   sat(cnf) -> satck(cnf, guess(cnf))
380.41/291.66	   satck(cnf, assign) -> if(verify(assign), assign, unsat)
380.41/291.66	
380.41/291.66	S is empty.
380.41/291.66	Rewrite Strategy: INNERMOST
380.48/291.71	EOF