22.25/7.18 WORST_CASE(Omega(n^1), O(n^1)) 22.25/7.19 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 22.25/7.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 22.25/7.19 22.25/7.19 22.25/7.19 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.25/7.19 22.25/7.19 (0) CpxTRS 22.25/7.19 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 22.25/7.19 (2) CpxTRS 22.25/7.19 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 22.25/7.19 (4) CpxTRS 22.25/7.19 (5) CpxTrsMatchBoundsTAProof [FINISHED, 99 ms] 22.25/7.19 (6) BOUNDS(1, n^1) 22.25/7.19 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 22.25/7.19 (8) TRS for Loop Detection 22.25/7.19 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 22.25/7.19 (10) BEST 22.25/7.19 (11) proven lower bound 22.25/7.19 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 22.25/7.19 (13) BOUNDS(n^1, INF) 22.25/7.19 (14) TRS for Loop Detection 22.25/7.19 22.25/7.19 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (0) 22.25/7.19 Obligation: 22.25/7.19 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.25/7.19 22.25/7.19 22.25/7.19 The TRS R consists of the following rules: 22.25/7.19 22.25/7.19 active(eq(0, 0)) -> mark(true) 22.25/7.19 active(eq(s(X), s(Y))) -> mark(eq(X, Y)) 22.25/7.19 active(eq(X, Y)) -> mark(false) 22.25/7.19 active(inf(X)) -> mark(cons(X, inf(s(X)))) 22.25/7.19 active(take(0, X)) -> mark(nil) 22.25/7.19 active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L))) 22.25/7.19 active(length(nil)) -> mark(0) 22.25/7.19 active(length(cons(X, L))) -> mark(s(length(L))) 22.25/7.19 active(inf(X)) -> inf(active(X)) 22.25/7.19 active(take(X1, X2)) -> take(active(X1), X2) 22.25/7.19 active(take(X1, X2)) -> take(X1, active(X2)) 22.25/7.19 active(length(X)) -> length(active(X)) 22.25/7.19 inf(mark(X)) -> mark(inf(X)) 22.25/7.19 take(mark(X1), X2) -> mark(take(X1, X2)) 22.25/7.19 take(X1, mark(X2)) -> mark(take(X1, X2)) 22.25/7.19 length(mark(X)) -> mark(length(X)) 22.25/7.19 proper(eq(X1, X2)) -> eq(proper(X1), proper(X2)) 22.25/7.19 proper(0) -> ok(0) 22.25/7.19 proper(true) -> ok(true) 22.25/7.19 proper(s(X)) -> s(proper(X)) 22.25/7.19 proper(false) -> ok(false) 22.25/7.19 proper(inf(X)) -> inf(proper(X)) 22.25/7.19 proper(cons(any(X1), X2)) -> cons(any(any(proper(X1))), any(proper(X2))) 22.25/7.19 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 22.25/7.19 proper(nil) -> ok(nil) 22.25/7.19 proper(length(X)) -> length(proper(X)) 22.25/7.19 eq(ok(X1), ok(X2)) -> ok(eq(X1, X2)) 22.25/7.19 s(ok(X)) -> ok(s(X)) 22.25/7.19 inf(ok(X)) -> ok(inf(X)) 22.25/7.19 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 22.25/7.19 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 22.25/7.19 length(ok(X)) -> ok(length(X)) 22.25/7.19 top(mark(X)) -> top(proper(X)) 22.25/7.19 top(ok(X)) -> top(active(X)) 22.25/7.19 any(X) -> s(X) 22.25/7.19 any(proper(X)) -> any(any(any(X))) 22.25/7.19 22.25/7.19 S is empty. 22.25/7.19 Rewrite Strategy: FULL 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 22.25/7.19 The following defined symbols can occur below the 0th argument of top: proper, active 22.25/7.19 The following defined symbols can occur below the 0th argument of proper: proper, active 22.25/7.19 The following defined symbols can occur below the 0th argument of active: proper, active 22.25/7.19 22.25/7.19 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 22.25/7.19 active(eq(0, 0)) -> mark(true) 22.25/7.19 active(eq(s(X), s(Y))) -> mark(eq(X, Y)) 22.25/7.19 active(eq(X, Y)) -> mark(false) 22.25/7.19 active(inf(X)) -> mark(cons(X, inf(s(X)))) 22.25/7.19 active(take(0, X)) -> mark(nil) 22.25/7.19 active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L))) 22.25/7.19 active(length(nil)) -> mark(0) 22.25/7.19 active(length(cons(X, L))) -> mark(s(length(L))) 22.25/7.19 active(inf(X)) -> inf(active(X)) 22.25/7.19 active(take(X1, X2)) -> take(active(X1), X2) 22.25/7.19 active(take(X1, X2)) -> take(X1, active(X2)) 22.25/7.19 active(length(X)) -> length(active(X)) 22.25/7.19 proper(eq(X1, X2)) -> eq(proper(X1), proper(X2)) 22.25/7.19 proper(s(X)) -> s(proper(X)) 22.25/7.19 proper(inf(X)) -> inf(proper(X)) 22.25/7.19 proper(cons(any(X1), X2)) -> cons(any(any(proper(X1))), any(proper(X2))) 22.25/7.19 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 22.25/7.19 proper(length(X)) -> length(proper(X)) 22.25/7.19 any(proper(X)) -> any(any(any(X))) 22.25/7.19 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (2) 22.25/7.19 Obligation: 22.25/7.19 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 22.25/7.19 22.25/7.19 22.25/7.19 The TRS R consists of the following rules: 22.25/7.19 22.25/7.19 inf(mark(X)) -> mark(inf(X)) 22.25/7.19 take(mark(X1), X2) -> mark(take(X1, X2)) 22.25/7.19 take(X1, mark(X2)) -> mark(take(X1, X2)) 22.25/7.19 length(mark(X)) -> mark(length(X)) 22.25/7.19 proper(0) -> ok(0) 22.25/7.19 proper(true) -> ok(true) 22.25/7.19 proper(false) -> ok(false) 22.25/7.19 proper(nil) -> ok(nil) 22.25/7.19 eq(ok(X1), ok(X2)) -> ok(eq(X1, X2)) 22.25/7.19 s(ok(X)) -> ok(s(X)) 22.25/7.19 inf(ok(X)) -> ok(inf(X)) 22.25/7.19 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 22.25/7.19 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 22.25/7.19 length(ok(X)) -> ok(length(X)) 22.25/7.19 top(mark(X)) -> top(proper(X)) 22.25/7.19 top(ok(X)) -> top(active(X)) 22.25/7.19 any(X) -> s(X) 22.25/7.19 22.25/7.19 S is empty. 22.25/7.19 Rewrite Strategy: FULL 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 22.25/7.19 transformed relative TRS to TRS 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (4) 22.25/7.19 Obligation: 22.25/7.19 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 22.25/7.19 22.25/7.19 22.25/7.19 The TRS R consists of the following rules: 22.25/7.19 22.25/7.19 inf(mark(X)) -> mark(inf(X)) 22.25/7.19 take(mark(X1), X2) -> mark(take(X1, X2)) 22.25/7.19 take(X1, mark(X2)) -> mark(take(X1, X2)) 22.25/7.19 length(mark(X)) -> mark(length(X)) 22.25/7.19 proper(0) -> ok(0) 22.25/7.19 proper(true) -> ok(true) 22.25/7.19 proper(false) -> ok(false) 22.25/7.19 proper(nil) -> ok(nil) 22.25/7.19 eq(ok(X1), ok(X2)) -> ok(eq(X1, X2)) 22.25/7.19 s(ok(X)) -> ok(s(X)) 22.25/7.19 inf(ok(X)) -> ok(inf(X)) 22.25/7.19 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 22.25/7.19 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 22.25/7.19 length(ok(X)) -> ok(length(X)) 22.25/7.19 top(mark(X)) -> top(proper(X)) 22.25/7.19 top(ok(X)) -> top(active(X)) 22.25/7.19 any(X) -> s(X) 22.25/7.19 22.25/7.19 S is empty. 22.25/7.19 Rewrite Strategy: FULL 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (5) CpxTrsMatchBoundsTAProof (FINISHED) 22.25/7.19 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 2. 22.25/7.19 22.25/7.19 The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 22.25/7.19 final states : [1, 2, 3, 4, 5, 6, 7, 8, 9] 22.25/7.19 transitions: 22.25/7.19 mark0(0) -> 0 22.25/7.19 00() -> 0 22.25/7.19 ok0(0) -> 0 22.25/7.19 true0() -> 0 22.25/7.19 false0() -> 0 22.25/7.19 nil0() -> 0 22.25/7.19 active0(0) -> 0 22.25/7.19 inf0(0) -> 1 22.25/7.19 take0(0, 0) -> 2 22.25/7.19 length0(0) -> 3 22.25/7.19 proper0(0) -> 4 22.25/7.19 eq0(0, 0) -> 5 22.25/7.19 s0(0) -> 6 22.25/7.19 cons0(0, 0) -> 7 22.25/7.19 top0(0) -> 8 22.25/7.19 any0(0) -> 9 22.25/7.19 inf1(0) -> 10 22.25/7.19 mark1(10) -> 1 22.25/7.19 take1(0, 0) -> 11 22.25/7.19 mark1(11) -> 2 22.25/7.19 length1(0) -> 12 22.25/7.19 mark1(12) -> 3 22.25/7.19 01() -> 13 22.25/7.19 ok1(13) -> 4 22.25/7.19 true1() -> 14 22.25/7.19 ok1(14) -> 4 22.25/7.19 false1() -> 15 22.25/7.19 ok1(15) -> 4 22.25/7.19 nil1() -> 16 22.25/7.19 ok1(16) -> 4 22.25/7.19 eq1(0, 0) -> 17 22.25/7.19 ok1(17) -> 5 22.25/7.19 s1(0) -> 18 22.25/7.19 ok1(18) -> 6 22.25/7.19 inf1(0) -> 19 22.25/7.19 ok1(19) -> 1 22.25/7.19 cons1(0, 0) -> 20 22.25/7.19 ok1(20) -> 7 22.25/7.19 take1(0, 0) -> 21 22.25/7.19 ok1(21) -> 2 22.25/7.19 length1(0) -> 22 22.25/7.19 ok1(22) -> 3 22.25/7.19 proper1(0) -> 23 22.25/7.19 top1(23) -> 8 22.25/7.19 active1(0) -> 24 22.25/7.19 top1(24) -> 8 22.25/7.19 s1(0) -> 9 22.25/7.19 mark1(10) -> 10 22.25/7.19 mark1(10) -> 19 22.25/7.19 mark1(11) -> 11 22.25/7.19 mark1(11) -> 21 22.25/7.19 mark1(12) -> 12 22.25/7.19 mark1(12) -> 22 22.25/7.19 ok1(13) -> 23 22.25/7.19 ok1(14) -> 23 22.25/7.19 ok1(15) -> 23 22.25/7.19 ok1(16) -> 23 22.25/7.19 ok1(17) -> 17 22.25/7.19 ok1(18) -> 9 22.25/7.19 ok1(18) -> 18 22.25/7.19 ok1(19) -> 10 22.25/7.19 ok1(19) -> 19 22.25/7.19 ok1(20) -> 20 22.25/7.19 ok1(21) -> 11 22.25/7.19 ok1(21) -> 21 22.25/7.19 ok1(22) -> 12 22.25/7.19 ok1(22) -> 22 22.25/7.19 active2(13) -> 25 22.25/7.19 top2(25) -> 8 22.25/7.19 active2(14) -> 25 22.25/7.19 active2(15) -> 25 22.25/7.19 active2(16) -> 25 22.25/7.19 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (6) 22.25/7.19 BOUNDS(1, n^1) 22.25/7.19 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (7) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 22.25/7.19 Transformed a relative TRS into a decreasing-loop problem. 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (8) 22.25/7.19 Obligation: 22.25/7.19 Analyzing the following TRS for decreasing loops: 22.25/7.19 22.25/7.19 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.25/7.19 22.25/7.19 22.25/7.19 The TRS R consists of the following rules: 22.25/7.19 22.25/7.19 active(eq(0, 0)) -> mark(true) 22.25/7.19 active(eq(s(X), s(Y))) -> mark(eq(X, Y)) 22.25/7.19 active(eq(X, Y)) -> mark(false) 22.25/7.19 active(inf(X)) -> mark(cons(X, inf(s(X)))) 22.25/7.19 active(take(0, X)) -> mark(nil) 22.25/7.19 active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L))) 22.25/7.19 active(length(nil)) -> mark(0) 22.25/7.19 active(length(cons(X, L))) -> mark(s(length(L))) 22.25/7.19 active(inf(X)) -> inf(active(X)) 22.25/7.19 active(take(X1, X2)) -> take(active(X1), X2) 22.25/7.19 active(take(X1, X2)) -> take(X1, active(X2)) 22.25/7.19 active(length(X)) -> length(active(X)) 22.25/7.19 inf(mark(X)) -> mark(inf(X)) 22.25/7.19 take(mark(X1), X2) -> mark(take(X1, X2)) 22.25/7.19 take(X1, mark(X2)) -> mark(take(X1, X2)) 22.25/7.19 length(mark(X)) -> mark(length(X)) 22.25/7.19 proper(eq(X1, X2)) -> eq(proper(X1), proper(X2)) 22.25/7.19 proper(0) -> ok(0) 22.25/7.19 proper(true) -> ok(true) 22.25/7.19 proper(s(X)) -> s(proper(X)) 22.25/7.19 proper(false) -> ok(false) 22.25/7.19 proper(inf(X)) -> inf(proper(X)) 22.25/7.19 proper(cons(any(X1), X2)) -> cons(any(any(proper(X1))), any(proper(X2))) 22.25/7.19 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 22.25/7.19 proper(nil) -> ok(nil) 22.25/7.19 proper(length(X)) -> length(proper(X)) 22.25/7.19 eq(ok(X1), ok(X2)) -> ok(eq(X1, X2)) 22.25/7.19 s(ok(X)) -> ok(s(X)) 22.25/7.19 inf(ok(X)) -> ok(inf(X)) 22.25/7.19 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 22.25/7.19 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 22.25/7.19 length(ok(X)) -> ok(length(X)) 22.25/7.19 top(mark(X)) -> top(proper(X)) 22.25/7.19 top(ok(X)) -> top(active(X)) 22.25/7.19 any(X) -> s(X) 22.25/7.19 any(proper(X)) -> any(any(any(X))) 22.25/7.19 22.25/7.19 S is empty. 22.25/7.19 Rewrite Strategy: FULL 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (9) DecreasingLoopProof (LOWER BOUND(ID)) 22.25/7.19 The following loop(s) give(s) rise to the lower bound Omega(n^1): 22.25/7.19 22.25/7.19 The rewrite sequence 22.25/7.19 22.25/7.19 take(ok(X1), ok(X2)) ->^+ ok(take(X1, X2)) 22.25/7.19 22.25/7.19 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 22.25/7.19 22.25/7.19 The pumping substitution is [X1 / ok(X1), X2 / ok(X2)]. 22.25/7.19 22.25/7.19 The result substitution is [ ]. 22.25/7.19 22.25/7.19 22.25/7.19 22.25/7.19 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (10) 22.25/7.19 Complex Obligation (BEST) 22.25/7.19 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (11) 22.25/7.19 Obligation: 22.25/7.19 Proved the lower bound n^1 for the following obligation: 22.25/7.19 22.25/7.19 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.25/7.19 22.25/7.19 22.25/7.19 The TRS R consists of the following rules: 22.25/7.19 22.25/7.19 active(eq(0, 0)) -> mark(true) 22.25/7.19 active(eq(s(X), s(Y))) -> mark(eq(X, Y)) 22.25/7.19 active(eq(X, Y)) -> mark(false) 22.25/7.19 active(inf(X)) -> mark(cons(X, inf(s(X)))) 22.25/7.19 active(take(0, X)) -> mark(nil) 22.25/7.19 active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L))) 22.25/7.19 active(length(nil)) -> mark(0) 22.25/7.19 active(length(cons(X, L))) -> mark(s(length(L))) 22.25/7.19 active(inf(X)) -> inf(active(X)) 22.25/7.19 active(take(X1, X2)) -> take(active(X1), X2) 22.25/7.19 active(take(X1, X2)) -> take(X1, active(X2)) 22.25/7.19 active(length(X)) -> length(active(X)) 22.25/7.19 inf(mark(X)) -> mark(inf(X)) 22.25/7.19 take(mark(X1), X2) -> mark(take(X1, X2)) 22.25/7.19 take(X1, mark(X2)) -> mark(take(X1, X2)) 22.25/7.19 length(mark(X)) -> mark(length(X)) 22.25/7.19 proper(eq(X1, X2)) -> eq(proper(X1), proper(X2)) 22.25/7.19 proper(0) -> ok(0) 22.25/7.19 proper(true) -> ok(true) 22.25/7.19 proper(s(X)) -> s(proper(X)) 22.25/7.19 proper(false) -> ok(false) 22.25/7.19 proper(inf(X)) -> inf(proper(X)) 22.25/7.19 proper(cons(any(X1), X2)) -> cons(any(any(proper(X1))), any(proper(X2))) 22.25/7.19 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 22.25/7.19 proper(nil) -> ok(nil) 22.25/7.19 proper(length(X)) -> length(proper(X)) 22.25/7.19 eq(ok(X1), ok(X2)) -> ok(eq(X1, X2)) 22.25/7.19 s(ok(X)) -> ok(s(X)) 22.25/7.19 inf(ok(X)) -> ok(inf(X)) 22.25/7.19 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 22.25/7.19 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 22.25/7.19 length(ok(X)) -> ok(length(X)) 22.25/7.19 top(mark(X)) -> top(proper(X)) 22.25/7.19 top(ok(X)) -> top(active(X)) 22.25/7.19 any(X) -> s(X) 22.25/7.19 any(proper(X)) -> any(any(any(X))) 22.25/7.19 22.25/7.19 S is empty. 22.25/7.19 Rewrite Strategy: FULL 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (12) LowerBoundPropagationProof (FINISHED) 22.25/7.19 Propagated lower bound. 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (13) 22.25/7.19 BOUNDS(n^1, INF) 22.25/7.19 22.25/7.19 ---------------------------------------- 22.25/7.19 22.25/7.19 (14) 22.25/7.19 Obligation: 22.25/7.19 Analyzing the following TRS for decreasing loops: 22.25/7.19 22.25/7.19 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.25/7.19 22.25/7.19 22.25/7.19 The TRS R consists of the following rules: 22.25/7.19 22.25/7.19 active(eq(0, 0)) -> mark(true) 22.25/7.19 active(eq(s(X), s(Y))) -> mark(eq(X, Y)) 22.25/7.19 active(eq(X, Y)) -> mark(false) 22.25/7.19 active(inf(X)) -> mark(cons(X, inf(s(X)))) 22.25/7.19 active(take(0, X)) -> mark(nil) 22.25/7.19 active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L))) 22.25/7.19 active(length(nil)) -> mark(0) 22.25/7.19 active(length(cons(X, L))) -> mark(s(length(L))) 22.25/7.19 active(inf(X)) -> inf(active(X)) 22.25/7.19 active(take(X1, X2)) -> take(active(X1), X2) 22.25/7.19 active(take(X1, X2)) -> take(X1, active(X2)) 22.25/7.19 active(length(X)) -> length(active(X)) 22.25/7.19 inf(mark(X)) -> mark(inf(X)) 22.25/7.19 take(mark(X1), X2) -> mark(take(X1, X2)) 22.25/7.19 take(X1, mark(X2)) -> mark(take(X1, X2)) 22.25/7.19 length(mark(X)) -> mark(length(X)) 22.25/7.19 proper(eq(X1, X2)) -> eq(proper(X1), proper(X2)) 22.25/7.19 proper(0) -> ok(0) 22.25/7.19 proper(true) -> ok(true) 22.25/7.19 proper(s(X)) -> s(proper(X)) 22.25/7.19 proper(false) -> ok(false) 22.25/7.19 proper(inf(X)) -> inf(proper(X)) 22.25/7.19 proper(cons(any(X1), X2)) -> cons(any(any(proper(X1))), any(proper(X2))) 22.25/7.19 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 22.25/7.19 proper(nil) -> ok(nil) 22.25/7.19 proper(length(X)) -> length(proper(X)) 22.25/7.19 eq(ok(X1), ok(X2)) -> ok(eq(X1, X2)) 22.25/7.19 s(ok(X)) -> ok(s(X)) 22.25/7.19 inf(ok(X)) -> ok(inf(X)) 22.25/7.19 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 22.25/7.19 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 22.25/7.19 length(ok(X)) -> ok(length(X)) 22.25/7.19 top(mark(X)) -> top(proper(X)) 22.25/7.19 top(ok(X)) -> top(active(X)) 22.25/7.19 any(X) -> s(X) 22.25/7.19 any(proper(X)) -> any(any(any(X))) 22.25/7.19 22.25/7.19 S is empty. 22.25/7.19 Rewrite Strategy: FULL 22.55/7.23 EOF