1046.43/291.52	WORST_CASE(Omega(n^1), O(n^1))
1046.43/291.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1046.43/291.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
1046.43/291.53	
1046.43/291.53	(0) CpxTRS
1046.43/291.53	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
1046.43/291.53	(2) CpxTRS
1046.43/291.53	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
1046.43/291.53	    (4) CpxTRS
1046.43/291.53	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 62 ms]
1046.43/291.53	    (6) BOUNDS(1, n^1)
1046.43/291.53	(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
1046.43/291.53	(8) CpxTRS
1046.43/291.53	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1046.43/291.53	    (10) typed CpxTrs
1046.43/291.53	    (11) OrderProof [LOWER BOUND(ID), 0 ms]
1046.43/291.53	    (12) typed CpxTrs
1046.43/291.53	    (13) RewriteLemmaProof [LOWER BOUND(ID), 471 ms]
1046.43/291.53	    (14) BEST
1046.43/291.53	        (15) proven lower bound
1046.43/291.53	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
1046.43/291.53	            (17) BOUNDS(n^1, INF)
1046.43/291.53	        (18) typed CpxTrs
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(0)
1046.43/291.53	Obligation:
1046.43/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	The TRS R consists of the following rules:
1046.43/291.53	
1046.43/291.53	   active(f(x)) -> mark(x)
1046.43/291.53	   top(active(c)) -> top(mark(c))
1046.43/291.53	   top(mark(x)) -> top(check(x))
1046.43/291.53	   check(f(x)) -> f(check(x))
1046.43/291.53	   check(x) -> start(match(f(X), x))
1046.43/291.53	   match(f(x), f(y)) -> f(match(x, y))
1046.43/291.53	   match(X, x) -> proper(x)
1046.43/291.53	   proper(c) -> ok(c)
1046.43/291.53	   proper(f(x)) -> f(proper(x))
1046.43/291.53	   f(ok(x)) -> ok(f(x))
1046.43/291.53	   start(ok(x)) -> found(x)
1046.43/291.53	   f(found(x)) -> found(f(x))
1046.43/291.53	   top(found(x)) -> top(active(x))
1046.43/291.53	   active(f(x)) -> f(active(x))
1046.43/291.53	   f(mark(x)) -> mark(f(x))
1046.43/291.53	
1046.43/291.53	S is empty.
1046.43/291.53	Rewrite Strategy: FULL
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
1046.43/291.53	The following defined symbols can occur below the 0th argument of top: active, start, proper, top, f, check, match
1046.43/291.53	The following defined symbols can occur below the 0th argument of active: active, start, proper, top, f, check, match
1046.43/291.53	The following defined symbols can occur below the 0th argument of f: active, start, proper, top, f, check, match
1046.43/291.53	The following defined symbols can occur below the 0th argument of start: active, start, proper, top, f, check, match
1046.43/291.53	The following defined symbols can occur below the 0th argument of match: active, start, proper, top, f, check, match
1046.43/291.53	The following defined symbols can occur below the 0th argument of check: active, start, proper, top, f, check, match
1046.43/291.53	
1046.43/291.53	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
1046.43/291.53	match(f(x), f(y)) -> f(match(x, y))
1046.43/291.53	proper(f(x)) -> f(proper(x))
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(2)
1046.43/291.53	Obligation:
1046.43/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	The TRS R consists of the following rules:
1046.43/291.53	
1046.43/291.53	   active(f(x)) -> mark(x)
1046.43/291.53	   top(active(c)) -> top(mark(c))
1046.43/291.53	   top(mark(x)) -> top(check(x))
1046.43/291.53	   check(f(x)) -> f(check(x))
1046.43/291.53	   check(x) -> start(match(f(X), x))
1046.43/291.53	   match(X, x) -> proper(x)
1046.43/291.53	   proper(c) -> ok(c)
1046.43/291.53	   f(ok(x)) -> ok(f(x))
1046.43/291.53	   start(ok(x)) -> found(x)
1046.43/291.53	   f(found(x)) -> found(f(x))
1046.43/291.53	   top(found(x)) -> top(active(x))
1046.43/291.53	   active(f(x)) -> f(active(x))
1046.43/291.53	   f(mark(x)) -> mark(f(x))
1046.43/291.53	
1046.43/291.53	S is empty.
1046.43/291.53	Rewrite Strategy: FULL
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(3) RelTrsToTrsProof (UPPER BOUND(ID))
1046.43/291.53	transformed relative TRS to TRS
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(4)
1046.43/291.53	Obligation:
1046.43/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	The TRS R consists of the following rules:
1046.43/291.53	
1046.43/291.53	   active(f(x)) -> mark(x)
1046.43/291.53	   top(active(c)) -> top(mark(c))
1046.43/291.53	   top(mark(x)) -> top(check(x))
1046.43/291.53	   check(f(x)) -> f(check(x))
1046.43/291.53	   check(x) -> start(match(f(X), x))
1046.43/291.53	   match(X, x) -> proper(x)
1046.43/291.53	   proper(c) -> ok(c)
1046.43/291.53	   f(ok(x)) -> ok(f(x))
1046.43/291.53	   start(ok(x)) -> found(x)
1046.43/291.53	   f(found(x)) -> found(f(x))
1046.43/291.53	   top(found(x)) -> top(active(x))
1046.43/291.53	   active(f(x)) -> f(active(x))
1046.43/291.53	   f(mark(x)) -> mark(f(x))
1046.43/291.53	
1046.43/291.53	S is empty.
1046.43/291.53	Rewrite Strategy: FULL
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(5) CpxTrsMatchBoundsTAProof (FINISHED)
1046.43/291.53	A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 3. 
1046.43/291.53	
1046.43/291.53	The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 
1046.43/291.53	final states : [1, 2, 3, 4, 5, 6, 7]
1046.43/291.53	transitions: 
1046.43/291.53	mark0(0) -> 0
1046.43/291.53	c0() -> 0
1046.43/291.53	X0() -> 0
1046.43/291.53	ok0(0) -> 0
1046.43/291.53	found0(0) -> 0
1046.43/291.53	active0(0) -> 1
1046.43/291.53	top0(0) -> 2
1046.43/291.53	check0(0) -> 3
1046.43/291.53	match0(0, 0) -> 4
1046.43/291.53	proper0(0) -> 5
1046.43/291.53	f0(0) -> 6
1046.43/291.53	start0(0) -> 7
1046.43/291.53	check1(0) -> 8
1046.43/291.53	top1(8) -> 2
1046.43/291.53	X1() -> 11
1046.43/291.53	f1(11) -> 10
1046.43/291.53	match1(10, 0) -> 9
1046.43/291.53	start1(9) -> 3
1046.43/291.53	proper1(0) -> 4
1046.43/291.53	c1() -> 12
1046.43/291.53	ok1(12) -> 5
1046.43/291.53	f1(0) -> 13
1046.43/291.53	ok1(13) -> 6
1046.43/291.53	found1(0) -> 7
1046.43/291.53	f1(0) -> 14
1046.43/291.53	found1(14) -> 6
1046.43/291.53	active1(0) -> 15
1046.43/291.53	top1(15) -> 2
1046.43/291.53	f1(0) -> 16
1046.43/291.53	mark1(16) -> 6
1046.43/291.53	c1() -> 18
1046.43/291.53	mark1(18) -> 17
1046.43/291.53	top1(17) -> 2
1046.43/291.53	X2() -> 21
1046.43/291.53	f2(21) -> 20
1046.43/291.53	match2(20, 0) -> 19
1046.43/291.53	start2(19) -> 8
1046.43/291.53	ok1(12) -> 4
1046.43/291.53	ok1(13) -> 13
1046.43/291.53	ok1(13) -> 14
1046.43/291.53	ok1(13) -> 16
1046.43/291.53	found1(14) -> 13
1046.43/291.53	found1(14) -> 14
1046.43/291.53	found1(14) -> 16
1046.43/291.53	mark1(16) -> 13
1046.43/291.53	mark1(16) -> 14
1046.43/291.53	mark1(16) -> 16
1046.43/291.53	check2(18) -> 22
1046.43/291.53	top2(22) -> 2
1046.43/291.53	X3() -> 25
1046.43/291.53	f3(25) -> 24
1046.43/291.53	match3(24, 18) -> 23
1046.43/291.53	start3(23) -> 22
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(6)
1046.43/291.53	BOUNDS(1, n^1)
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(7) RenamingProof (BOTH BOUNDS(ID, ID))
1046.43/291.53	Renamed function symbols to avoid clashes with predefined symbol.
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(8)
1046.43/291.53	Obligation:
1046.43/291.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	The TRS R consists of the following rules:
1046.43/291.53	
1046.43/291.53	   active(f(x)) -> mark(x)
1046.43/291.53	   top(active(c)) -> top(mark(c))
1046.43/291.53	   top(mark(x)) -> top(check(x))
1046.43/291.53	   check(f(x)) -> f(check(x))
1046.43/291.53	   check(x) -> start(match(f(X), x))
1046.43/291.53	   match(f(x), f(y)) -> f(match(x, y))
1046.43/291.53	   match(X, x) -> proper(x)
1046.43/291.53	   proper(c) -> ok(c)
1046.43/291.53	   proper(f(x)) -> f(proper(x))
1046.43/291.53	   f(ok(x)) -> ok(f(x))
1046.43/291.53	   start(ok(x)) -> found(x)
1046.43/291.53	   f(found(x)) -> found(f(x))
1046.43/291.53	   top(found(x)) -> top(active(x))
1046.43/291.53	   active(f(x)) -> f(active(x))
1046.43/291.53	   f(mark(x)) -> mark(f(x))
1046.43/291.53	
1046.43/291.53	S is empty.
1046.43/291.53	Rewrite Strategy: FULL
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(9) TypeInferenceProof (BOTH BOUNDS(ID, ID))
1046.43/291.53	Infered types.
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(10)
1046.43/291.53	Obligation:
1046.43/291.53	TRS:
1046.43/291.53	Rules:
1046.43/291.53	active(f(x)) -> mark(x)
1046.43/291.53	top(active(c)) -> top(mark(c))
1046.43/291.53	top(mark(x)) -> top(check(x))
1046.43/291.53	check(f(x)) -> f(check(x))
1046.43/291.53	check(x) -> start(match(f(X), x))
1046.43/291.53	match(f(x), f(y)) -> f(match(x, y))
1046.43/291.53	match(X, x) -> proper(x)
1046.43/291.53	proper(c) -> ok(c)
1046.43/291.53	proper(f(x)) -> f(proper(x))
1046.43/291.53	f(ok(x)) -> ok(f(x))
1046.43/291.53	start(ok(x)) -> found(x)
1046.43/291.53	f(found(x)) -> found(f(x))
1046.43/291.53	top(found(x)) -> top(active(x))
1046.43/291.53	active(f(x)) -> f(active(x))
1046.43/291.53	f(mark(x)) -> mark(f(x))
1046.43/291.53	
1046.43/291.53	Types:
1046.43/291.53	active :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	f :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	mark :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	top :: mark:c:X:ok:found -> top
1046.43/291.53	c :: mark:c:X:ok:found
1046.43/291.53	check :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	start :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	match :: mark:c:X:ok:found -> mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	X :: mark:c:X:ok:found
1046.43/291.53	proper :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	ok :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	found :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	hole_mark:c:X:ok:found1_0 :: mark:c:X:ok:found
1046.43/291.53	hole_top2_0 :: top
1046.43/291.53	gen_mark:c:X:ok:found3_0 :: Nat -> mark:c:X:ok:found
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(11) OrderProof (LOWER BOUND(ID))
1046.43/291.53	Heuristically decided to analyse the following defined symbols:
1046.43/291.53	top, check, f, match, proper, active
1046.43/291.53	
1046.43/291.53	They will be analysed ascendingly in the following order:
1046.43/291.53	check < top
1046.43/291.53	active < top
1046.43/291.53	f < check
1046.43/291.53	match < check
1046.43/291.53	f < match
1046.43/291.53	f < proper
1046.43/291.53	f < active
1046.43/291.53	proper < match
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(12)
1046.43/291.53	Obligation:
1046.43/291.53	TRS:
1046.43/291.53	Rules:
1046.43/291.53	active(f(x)) -> mark(x)
1046.43/291.53	top(active(c)) -> top(mark(c))
1046.43/291.53	top(mark(x)) -> top(check(x))
1046.43/291.53	check(f(x)) -> f(check(x))
1046.43/291.53	check(x) -> start(match(f(X), x))
1046.43/291.53	match(f(x), f(y)) -> f(match(x, y))
1046.43/291.53	match(X, x) -> proper(x)
1046.43/291.53	proper(c) -> ok(c)
1046.43/291.53	proper(f(x)) -> f(proper(x))
1046.43/291.53	f(ok(x)) -> ok(f(x))
1046.43/291.53	start(ok(x)) -> found(x)
1046.43/291.53	f(found(x)) -> found(f(x))
1046.43/291.53	top(found(x)) -> top(active(x))
1046.43/291.53	active(f(x)) -> f(active(x))
1046.43/291.53	f(mark(x)) -> mark(f(x))
1046.43/291.53	
1046.43/291.53	Types:
1046.43/291.53	active :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	f :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	mark :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	top :: mark:c:X:ok:found -> top
1046.43/291.53	c :: mark:c:X:ok:found
1046.43/291.53	check :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	start :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	match :: mark:c:X:ok:found -> mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	X :: mark:c:X:ok:found
1046.43/291.53	proper :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	ok :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	found :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	hole_mark:c:X:ok:found1_0 :: mark:c:X:ok:found
1046.43/291.53	hole_top2_0 :: top
1046.43/291.53	gen_mark:c:X:ok:found3_0 :: Nat -> mark:c:X:ok:found
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	Generator Equations:
1046.43/291.53	gen_mark:c:X:ok:found3_0(0) <=> c
1046.43/291.53	gen_mark:c:X:ok:found3_0(+(x, 1)) <=> mark(gen_mark:c:X:ok:found3_0(x))
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	The following defined symbols remain to be analysed:
1046.43/291.53	f, top, check, match, proper, active
1046.43/291.53	
1046.43/291.53	They will be analysed ascendingly in the following order:
1046.43/291.53	check < top
1046.43/291.53	active < top
1046.43/291.53	f < check
1046.43/291.53	match < check
1046.43/291.53	f < match
1046.43/291.53	f < proper
1046.43/291.53	f < active
1046.43/291.53	proper < match
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(13) RewriteLemmaProof (LOWER BOUND(ID))
1046.43/291.53	Proved the following rewrite lemma:
1046.43/291.53	f(gen_mark:c:X:ok:found3_0(+(1, n5_0))) -> *4_0, rt in Omega(n5_0)
1046.43/291.53	
1046.43/291.53	Induction Base:
1046.43/291.53	f(gen_mark:c:X:ok:found3_0(+(1, 0)))
1046.43/291.53	
1046.43/291.53	Induction Step:
1046.43/291.53	f(gen_mark:c:X:ok:found3_0(+(1, +(n5_0, 1)))) ->_R^Omega(1)
1046.43/291.53	mark(f(gen_mark:c:X:ok:found3_0(+(1, n5_0)))) ->_IH
1046.43/291.53	mark(*4_0)
1046.43/291.53	
1046.43/291.53	We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(14)
1046.43/291.53	Complex Obligation (BEST)
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(15)
1046.43/291.53	Obligation:
1046.43/291.53	Proved the lower bound n^1 for the following obligation:
1046.43/291.53	
1046.43/291.53	TRS:
1046.43/291.53	Rules:
1046.43/291.53	active(f(x)) -> mark(x)
1046.43/291.53	top(active(c)) -> top(mark(c))
1046.43/291.53	top(mark(x)) -> top(check(x))
1046.43/291.53	check(f(x)) -> f(check(x))
1046.43/291.53	check(x) -> start(match(f(X), x))
1046.43/291.53	match(f(x), f(y)) -> f(match(x, y))
1046.43/291.53	match(X, x) -> proper(x)
1046.43/291.53	proper(c) -> ok(c)
1046.43/291.53	proper(f(x)) -> f(proper(x))
1046.43/291.53	f(ok(x)) -> ok(f(x))
1046.43/291.53	start(ok(x)) -> found(x)
1046.43/291.53	f(found(x)) -> found(f(x))
1046.43/291.53	top(found(x)) -> top(active(x))
1046.43/291.53	active(f(x)) -> f(active(x))
1046.43/291.53	f(mark(x)) -> mark(f(x))
1046.43/291.53	
1046.43/291.53	Types:
1046.43/291.53	active :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	f :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	mark :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	top :: mark:c:X:ok:found -> top
1046.43/291.53	c :: mark:c:X:ok:found
1046.43/291.53	check :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	start :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	match :: mark:c:X:ok:found -> mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	X :: mark:c:X:ok:found
1046.43/291.53	proper :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	ok :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	found :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	hole_mark:c:X:ok:found1_0 :: mark:c:X:ok:found
1046.43/291.53	hole_top2_0 :: top
1046.43/291.53	gen_mark:c:X:ok:found3_0 :: Nat -> mark:c:X:ok:found
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	Generator Equations:
1046.43/291.53	gen_mark:c:X:ok:found3_0(0) <=> c
1046.43/291.53	gen_mark:c:X:ok:found3_0(+(x, 1)) <=> mark(gen_mark:c:X:ok:found3_0(x))
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	The following defined symbols remain to be analysed:
1046.43/291.53	f, top, check, match, proper, active
1046.43/291.53	
1046.43/291.53	They will be analysed ascendingly in the following order:
1046.43/291.53	check < top
1046.43/291.53	active < top
1046.43/291.53	f < check
1046.43/291.53	match < check
1046.43/291.53	f < match
1046.43/291.53	f < proper
1046.43/291.53	f < active
1046.43/291.53	proper < match
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(16) LowerBoundPropagationProof (FINISHED)
1046.43/291.53	Propagated lower bound.
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(17)
1046.43/291.53	BOUNDS(n^1, INF)
1046.43/291.53	
1046.43/291.53	----------------------------------------
1046.43/291.53	
1046.43/291.53	(18)
1046.43/291.53	Obligation:
1046.43/291.53	TRS:
1046.43/291.53	Rules:
1046.43/291.53	active(f(x)) -> mark(x)
1046.43/291.53	top(active(c)) -> top(mark(c))
1046.43/291.53	top(mark(x)) -> top(check(x))
1046.43/291.53	check(f(x)) -> f(check(x))
1046.43/291.53	check(x) -> start(match(f(X), x))
1046.43/291.53	match(f(x), f(y)) -> f(match(x, y))
1046.43/291.53	match(X, x) -> proper(x)
1046.43/291.53	proper(c) -> ok(c)
1046.43/291.53	proper(f(x)) -> f(proper(x))
1046.43/291.53	f(ok(x)) -> ok(f(x))
1046.43/291.53	start(ok(x)) -> found(x)
1046.43/291.53	f(found(x)) -> found(f(x))
1046.43/291.53	top(found(x)) -> top(active(x))
1046.43/291.53	active(f(x)) -> f(active(x))
1046.43/291.53	f(mark(x)) -> mark(f(x))
1046.43/291.53	
1046.43/291.53	Types:
1046.43/291.53	active :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	f :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	mark :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	top :: mark:c:X:ok:found -> top
1046.43/291.53	c :: mark:c:X:ok:found
1046.43/291.53	check :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	start :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	match :: mark:c:X:ok:found -> mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	X :: mark:c:X:ok:found
1046.43/291.53	proper :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	ok :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	found :: mark:c:X:ok:found -> mark:c:X:ok:found
1046.43/291.53	hole_mark:c:X:ok:found1_0 :: mark:c:X:ok:found
1046.43/291.53	hole_top2_0 :: top
1046.43/291.53	gen_mark:c:X:ok:found3_0 :: Nat -> mark:c:X:ok:found
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	Lemmas:
1046.43/291.53	f(gen_mark:c:X:ok:found3_0(+(1, n5_0))) -> *4_0, rt in Omega(n5_0)
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	Generator Equations:
1046.43/291.53	gen_mark:c:X:ok:found3_0(0) <=> c
1046.43/291.53	gen_mark:c:X:ok:found3_0(+(x, 1)) <=> mark(gen_mark:c:X:ok:found3_0(x))
1046.43/291.53	
1046.43/291.53	
1046.43/291.53	The following defined symbols remain to be analysed:
1046.43/291.53	proper, top, check, match, active
1046.43/291.53	
1046.43/291.53	They will be analysed ascendingly in the following order:
1046.43/291.53	check < top
1046.43/291.53	active < top
1046.43/291.53	match < check
1046.43/291.53	proper < match
1046.52/291.59	EOF