23.47/7.99 WORST_CASE(Omega(n^1), O(n^1)) 23.47/8.00 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 23.47/8.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 23.47/8.00 23.47/8.00 23.47/8.00 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 23.47/8.00 23.47/8.00 (0) CpxTRS 23.47/8.00 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 23.47/8.00 (2) CpxTRS 23.47/8.00 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 23.47/8.00 (4) CpxTRS 23.47/8.00 (5) CpxTrsMatchBoundsTAProof [FINISHED, 143 ms] 23.47/8.00 (6) BOUNDS(1, n^1) 23.47/8.00 (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 23.47/8.00 (8) CpxTRS 23.47/8.00 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 23.47/8.00 (10) typed CpxTrs 23.47/8.00 (11) OrderProof [LOWER BOUND(ID), 0 ms] 23.47/8.00 (12) typed CpxTrs 23.47/8.00 (13) RewriteLemmaProof [LOWER BOUND(ID), 463 ms] 23.47/8.00 (14) BEST 23.47/8.00 (15) proven lower bound 23.47/8.00 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 23.47/8.00 (17) BOUNDS(n^1, INF) 23.47/8.00 (18) typed CpxTrs 23.47/8.00 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (0) 23.47/8.00 Obligation: 23.47/8.00 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 23.47/8.00 23.47/8.00 23.47/8.00 The TRS R consists of the following rules: 23.47/8.00 23.47/8.00 active(f(a, b, X)) -> mark(f(X, X, X)) 23.47/8.00 active(c) -> mark(a) 23.47/8.00 active(c) -> mark(b) 23.47/8.00 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 23.47/8.00 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 23.47/8.00 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 23.47/8.00 proper(a) -> ok(a) 23.47/8.00 proper(b) -> ok(b) 23.47/8.00 proper(c) -> ok(c) 23.47/8.00 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 23.47/8.00 top(mark(X)) -> top(proper(X)) 23.47/8.00 top(ok(X)) -> top(active(X)) 23.47/8.00 23.47/8.00 S is empty. 23.47/8.00 Rewrite Strategy: FULL 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 23.47/8.00 The following defined symbols can occur below the 0th argument of top: proper, active 23.47/8.00 The following defined symbols can occur below the 0th argument of proper: proper, active 23.47/8.00 The following defined symbols can occur below the 0th argument of active: proper, active 23.47/8.00 23.47/8.00 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 23.47/8.00 active(f(a, b, X)) -> mark(f(X, X, X)) 23.47/8.00 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 23.47/8.00 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (2) 23.47/8.00 Obligation: 23.47/8.00 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 23.47/8.00 23.47/8.00 23.47/8.00 The TRS R consists of the following rules: 23.47/8.00 23.47/8.00 active(c) -> mark(a) 23.47/8.00 active(c) -> mark(b) 23.47/8.00 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 23.47/8.00 proper(a) -> ok(a) 23.47/8.00 proper(b) -> ok(b) 23.47/8.00 proper(c) -> ok(c) 23.47/8.00 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 23.47/8.00 top(mark(X)) -> top(proper(X)) 23.47/8.00 top(ok(X)) -> top(active(X)) 23.47/8.00 23.47/8.00 S is empty. 23.47/8.00 Rewrite Strategy: FULL 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 23.47/8.00 transformed relative TRS to TRS 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (4) 23.47/8.00 Obligation: 23.47/8.00 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 23.47/8.00 23.47/8.00 23.47/8.00 The TRS R consists of the following rules: 23.47/8.00 23.47/8.00 active(c) -> mark(a) 23.47/8.00 active(c) -> mark(b) 23.47/8.00 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 23.47/8.00 proper(a) -> ok(a) 23.47/8.00 proper(b) -> ok(b) 23.47/8.00 proper(c) -> ok(c) 23.47/8.00 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 23.47/8.00 top(mark(X)) -> top(proper(X)) 23.47/8.00 top(ok(X)) -> top(active(X)) 23.47/8.00 23.47/8.00 S is empty. 23.47/8.00 Rewrite Strategy: FULL 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (5) CpxTrsMatchBoundsTAProof (FINISHED) 23.47/8.00 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 4. 23.47/8.00 23.47/8.00 The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 23.47/8.00 final states : [1, 2, 3, 4] 23.47/8.00 transitions: 23.47/8.00 c0() -> 0 23.47/8.00 mark0(0) -> 0 23.47/8.00 a0() -> 0 23.47/8.00 b0() -> 0 23.47/8.00 ok0(0) -> 0 23.47/8.00 active0(0) -> 1 23.47/8.00 f0(0, 0, 0) -> 2 23.47/8.00 proper0(0) -> 3 23.47/8.00 top0(0) -> 4 23.47/8.00 a1() -> 5 23.47/8.00 mark1(5) -> 1 23.47/8.00 b1() -> 6 23.47/8.00 mark1(6) -> 1 23.47/8.00 f1(0, 0, 0) -> 7 23.47/8.00 mark1(7) -> 2 23.47/8.00 a1() -> 8 23.47/8.00 ok1(8) -> 3 23.47/8.00 b1() -> 9 23.47/8.00 ok1(9) -> 3 23.47/8.00 c1() -> 10 23.47/8.00 ok1(10) -> 3 23.47/8.00 f1(0, 0, 0) -> 11 23.47/8.00 ok1(11) -> 2 23.47/8.00 proper1(0) -> 12 23.47/8.00 top1(12) -> 4 23.47/8.00 active1(0) -> 13 23.47/8.00 top1(13) -> 4 23.47/8.00 mark1(5) -> 13 23.47/8.00 mark1(6) -> 13 23.47/8.00 mark1(7) -> 7 23.47/8.00 mark1(7) -> 11 23.47/8.00 ok1(8) -> 12 23.47/8.00 ok1(9) -> 12 23.47/8.00 ok1(10) -> 12 23.47/8.00 ok1(11) -> 7 23.47/8.00 ok1(11) -> 11 23.47/8.00 proper2(5) -> 14 23.47/8.00 top2(14) -> 4 23.47/8.00 proper2(6) -> 14 23.47/8.00 active2(8) -> 15 23.47/8.00 top2(15) -> 4 23.47/8.00 active2(9) -> 15 23.47/8.00 active2(10) -> 15 23.47/8.00 a2() -> 16 23.47/8.00 mark2(16) -> 15 23.47/8.00 b2() -> 17 23.47/8.00 mark2(17) -> 15 23.47/8.00 a2() -> 18 23.47/8.00 ok2(18) -> 14 23.47/8.00 b2() -> 19 23.47/8.00 ok2(19) -> 14 23.47/8.00 proper3(16) -> 20 23.47/8.00 top3(20) -> 4 23.47/8.00 proper3(17) -> 20 23.47/8.00 active3(18) -> 21 23.47/8.00 top3(21) -> 4 23.47/8.00 active3(19) -> 21 23.47/8.00 a3() -> 22 23.47/8.00 ok3(22) -> 20 23.47/8.00 b3() -> 23 23.47/8.00 ok3(23) -> 20 23.47/8.00 active4(22) -> 24 23.47/8.00 top4(24) -> 4 23.47/8.00 active4(23) -> 24 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (6) 23.47/8.00 BOUNDS(1, n^1) 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (7) RenamingProof (BOTH BOUNDS(ID, ID)) 23.47/8.00 Renamed function symbols to avoid clashes with predefined symbol. 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (8) 23.47/8.00 Obligation: 23.47/8.00 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 23.47/8.00 23.47/8.00 23.47/8.00 The TRS R consists of the following rules: 23.47/8.00 23.47/8.00 active(f(a, b, X)) -> mark(f(X, X, X)) 23.47/8.00 active(c) -> mark(a) 23.47/8.00 active(c) -> mark(b) 23.47/8.00 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 23.47/8.00 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 23.47/8.00 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 23.47/8.00 proper(a) -> ok(a) 23.47/8.00 proper(b) -> ok(b) 23.47/8.00 proper(c) -> ok(c) 23.47/8.00 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 23.47/8.00 top(mark(X)) -> top(proper(X)) 23.47/8.00 top(ok(X)) -> top(active(X)) 23.47/8.00 23.47/8.00 S is empty. 23.47/8.00 Rewrite Strategy: FULL 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 23.47/8.00 Infered types. 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (10) 23.47/8.00 Obligation: 23.47/8.00 TRS: 23.47/8.00 Rules: 23.47/8.00 active(f(a, b, X)) -> mark(f(X, X, X)) 23.47/8.00 active(c) -> mark(a) 23.47/8.00 active(c) -> mark(b) 23.47/8.00 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 23.47/8.00 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 23.47/8.00 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 23.47/8.00 proper(a) -> ok(a) 23.47/8.00 proper(b) -> ok(b) 23.47/8.00 proper(c) -> ok(c) 23.47/8.00 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 23.47/8.00 top(mark(X)) -> top(proper(X)) 23.47/8.00 top(ok(X)) -> top(active(X)) 23.47/8.00 23.47/8.00 Types: 23.47/8.00 active :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 f :: a:b:mark:c:ok -> a:b:mark:c:ok -> a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 a :: a:b:mark:c:ok 23.47/8.00 b :: a:b:mark:c:ok 23.47/8.00 mark :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 c :: a:b:mark:c:ok 23.47/8.00 proper :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 ok :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 top :: a:b:mark:c:ok -> top 23.47/8.00 hole_a:b:mark:c:ok1_0 :: a:b:mark:c:ok 23.47/8.00 hole_top2_0 :: top 23.47/8.00 gen_a:b:mark:c:ok3_0 :: Nat -> a:b:mark:c:ok 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (11) OrderProof (LOWER BOUND(ID)) 23.47/8.00 Heuristically decided to analyse the following defined symbols: 23.47/8.00 active, f, proper, top 23.47/8.00 23.47/8.00 They will be analysed ascendingly in the following order: 23.47/8.00 f < active 23.47/8.00 active < top 23.47/8.00 f < proper 23.47/8.00 proper < top 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (12) 23.47/8.00 Obligation: 23.47/8.00 TRS: 23.47/8.00 Rules: 23.47/8.00 active(f(a, b, X)) -> mark(f(X, X, X)) 23.47/8.00 active(c) -> mark(a) 23.47/8.00 active(c) -> mark(b) 23.47/8.00 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 23.47/8.00 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 23.47/8.00 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 23.47/8.00 proper(a) -> ok(a) 23.47/8.00 proper(b) -> ok(b) 23.47/8.00 proper(c) -> ok(c) 23.47/8.00 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 23.47/8.00 top(mark(X)) -> top(proper(X)) 23.47/8.00 top(ok(X)) -> top(active(X)) 23.47/8.00 23.47/8.00 Types: 23.47/8.00 active :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 f :: a:b:mark:c:ok -> a:b:mark:c:ok -> a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 a :: a:b:mark:c:ok 23.47/8.00 b :: a:b:mark:c:ok 23.47/8.00 mark :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 c :: a:b:mark:c:ok 23.47/8.00 proper :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 ok :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 top :: a:b:mark:c:ok -> top 23.47/8.00 hole_a:b:mark:c:ok1_0 :: a:b:mark:c:ok 23.47/8.00 hole_top2_0 :: top 23.47/8.00 gen_a:b:mark:c:ok3_0 :: Nat -> a:b:mark:c:ok 23.47/8.00 23.47/8.00 23.47/8.00 Generator Equations: 23.47/8.00 gen_a:b:mark:c:ok3_0(0) <=> a 23.47/8.00 gen_a:b:mark:c:ok3_0(+(x, 1)) <=> mark(gen_a:b:mark:c:ok3_0(x)) 23.47/8.00 23.47/8.00 23.47/8.00 The following defined symbols remain to be analysed: 23.47/8.00 f, active, proper, top 23.47/8.00 23.47/8.00 They will be analysed ascendingly in the following order: 23.47/8.00 f < active 23.47/8.00 active < top 23.47/8.00 f < proper 23.47/8.00 proper < top 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (13) RewriteLemmaProof (LOWER BOUND(ID)) 23.47/8.00 Proved the following rewrite lemma: 23.47/8.00 f(gen_a:b:mark:c:ok3_0(a), gen_a:b:mark:c:ok3_0(b), gen_a:b:mark:c:ok3_0(+(1, n5_0))) -> *4_0, rt in Omega(n5_0) 23.47/8.00 23.47/8.00 Induction Base: 23.47/8.00 f(gen_a:b:mark:c:ok3_0(a), gen_a:b:mark:c:ok3_0(b), gen_a:b:mark:c:ok3_0(+(1, 0))) 23.47/8.00 23.47/8.00 Induction Step: 23.47/8.00 f(gen_a:b:mark:c:ok3_0(a), gen_a:b:mark:c:ok3_0(b), gen_a:b:mark:c:ok3_0(+(1, +(n5_0, 1)))) ->_R^Omega(1) 23.47/8.00 mark(f(gen_a:b:mark:c:ok3_0(a), gen_a:b:mark:c:ok3_0(b), gen_a:b:mark:c:ok3_0(+(1, n5_0)))) ->_IH 23.47/8.00 mark(*4_0) 23.47/8.00 23.47/8.00 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (14) 23.47/8.00 Complex Obligation (BEST) 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (15) 23.47/8.00 Obligation: 23.47/8.00 Proved the lower bound n^1 for the following obligation: 23.47/8.00 23.47/8.00 TRS: 23.47/8.00 Rules: 23.47/8.00 active(f(a, b, X)) -> mark(f(X, X, X)) 23.47/8.00 active(c) -> mark(a) 23.47/8.00 active(c) -> mark(b) 23.47/8.00 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 23.47/8.00 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 23.47/8.00 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 23.47/8.00 proper(a) -> ok(a) 23.47/8.00 proper(b) -> ok(b) 23.47/8.00 proper(c) -> ok(c) 23.47/8.00 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 23.47/8.00 top(mark(X)) -> top(proper(X)) 23.47/8.00 top(ok(X)) -> top(active(X)) 23.47/8.00 23.47/8.00 Types: 23.47/8.00 active :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 f :: a:b:mark:c:ok -> a:b:mark:c:ok -> a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 a :: a:b:mark:c:ok 23.47/8.00 b :: a:b:mark:c:ok 23.47/8.00 mark :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 c :: a:b:mark:c:ok 23.47/8.00 proper :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 ok :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 top :: a:b:mark:c:ok -> top 23.47/8.00 hole_a:b:mark:c:ok1_0 :: a:b:mark:c:ok 23.47/8.00 hole_top2_0 :: top 23.47/8.00 gen_a:b:mark:c:ok3_0 :: Nat -> a:b:mark:c:ok 23.47/8.00 23.47/8.00 23.47/8.00 Generator Equations: 23.47/8.00 gen_a:b:mark:c:ok3_0(0) <=> a 23.47/8.00 gen_a:b:mark:c:ok3_0(+(x, 1)) <=> mark(gen_a:b:mark:c:ok3_0(x)) 23.47/8.00 23.47/8.00 23.47/8.00 The following defined symbols remain to be analysed: 23.47/8.00 f, active, proper, top 23.47/8.00 23.47/8.00 They will be analysed ascendingly in the following order: 23.47/8.00 f < active 23.47/8.00 active < top 23.47/8.00 f < proper 23.47/8.00 proper < top 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (16) LowerBoundPropagationProof (FINISHED) 23.47/8.00 Propagated lower bound. 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (17) 23.47/8.00 BOUNDS(n^1, INF) 23.47/8.00 23.47/8.00 ---------------------------------------- 23.47/8.00 23.47/8.00 (18) 23.47/8.00 Obligation: 23.47/8.00 TRS: 23.47/8.00 Rules: 23.47/8.00 active(f(a, b, X)) -> mark(f(X, X, X)) 23.47/8.00 active(c) -> mark(a) 23.47/8.00 active(c) -> mark(b) 23.47/8.00 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 23.47/8.00 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 23.47/8.00 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 23.47/8.00 proper(a) -> ok(a) 23.47/8.00 proper(b) -> ok(b) 23.47/8.00 proper(c) -> ok(c) 23.47/8.00 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 23.47/8.00 top(mark(X)) -> top(proper(X)) 23.47/8.00 top(ok(X)) -> top(active(X)) 23.47/8.00 23.47/8.00 Types: 23.47/8.00 active :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 f :: a:b:mark:c:ok -> a:b:mark:c:ok -> a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 a :: a:b:mark:c:ok 23.47/8.00 b :: a:b:mark:c:ok 23.47/8.00 mark :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 c :: a:b:mark:c:ok 23.47/8.00 proper :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 ok :: a:b:mark:c:ok -> a:b:mark:c:ok 23.47/8.00 top :: a:b:mark:c:ok -> top 23.47/8.00 hole_a:b:mark:c:ok1_0 :: a:b:mark:c:ok 23.47/8.00 hole_top2_0 :: top 23.47/8.00 gen_a:b:mark:c:ok3_0 :: Nat -> a:b:mark:c:ok 23.47/8.00 23.47/8.00 23.47/8.00 Lemmas: 23.47/8.00 f(gen_a:b:mark:c:ok3_0(a), gen_a:b:mark:c:ok3_0(b), gen_a:b:mark:c:ok3_0(+(1, n5_0))) -> *4_0, rt in Omega(n5_0) 23.47/8.00 23.47/8.00 23.47/8.00 Generator Equations: 23.47/8.00 gen_a:b:mark:c:ok3_0(0) <=> a 23.47/8.00 gen_a:b:mark:c:ok3_0(+(x, 1)) <=> mark(gen_a:b:mark:c:ok3_0(x)) 23.47/8.00 23.47/8.00 23.47/8.00 The following defined symbols remain to be analysed: 23.47/8.00 active, proper, top 23.47/8.00 23.47/8.00 They will be analysed ascendingly in the following order: 23.47/8.00 active < top 23.47/8.00 proper < top 23.81/8.04 EOF