29.39/9.78 WORST_CASE(Omega(n^1), O(n^1)) 29.39/9.79 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 29.39/9.79 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 29.39/9.79 29.39/9.79 29.39/9.79 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.39/9.79 29.39/9.79 (0) CpxTRS 29.39/9.79 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 29.39/9.79 (2) CpxTRS 29.39/9.79 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 29.39/9.79 (4) CpxTRS 29.39/9.79 (5) CpxTrsMatchBoundsTAProof [FINISHED, 77 ms] 29.39/9.79 (6) BOUNDS(1, n^1) 29.39/9.79 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 29.39/9.79 (8) TRS for Loop Detection 29.39/9.79 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 29.39/9.79 (10) BEST 29.39/9.79 (11) proven lower bound 29.39/9.79 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 29.39/9.79 (13) BOUNDS(n^1, INF) 29.39/9.79 (14) TRS for Loop Detection 29.39/9.79 29.39/9.79 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (0) 29.39/9.79 Obligation: 29.39/9.79 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.39/9.79 29.39/9.79 29.39/9.79 The TRS R consists of the following rules: 29.39/9.79 29.39/9.79 active(app(nil, YS)) -> mark(YS) 29.39/9.79 active(app(cons(X, XS), YS)) -> mark(cons(X, app(XS, YS))) 29.39/9.79 active(from(X)) -> mark(cons(X, from(s(X)))) 29.39/9.79 active(zWadr(nil, YS)) -> mark(nil) 29.39/9.79 active(zWadr(XS, nil)) -> mark(nil) 29.39/9.79 active(zWadr(cons(X, XS), cons(Y, YS))) -> mark(cons(app(Y, cons(X, nil)), zWadr(XS, YS))) 29.39/9.79 active(prefix(L)) -> mark(cons(nil, zWadr(L, prefix(L)))) 29.39/9.79 active(app(X1, X2)) -> app(active(X1), X2) 29.39/9.79 active(app(X1, X2)) -> app(X1, active(X2)) 29.39/9.79 active(cons(X1, X2)) -> cons(active(X1), X2) 29.39/9.79 active(from(X)) -> from(active(X)) 29.39/9.79 active(s(X)) -> s(active(X)) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(active(X1), X2) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(X1, active(X2)) 29.39/9.79 active(prefix(X)) -> prefix(active(X)) 29.39/9.79 app(mark(X1), X2) -> mark(app(X1, X2)) 29.39/9.79 app(X1, mark(X2)) -> mark(app(X1, X2)) 29.39/9.79 cons(mark(X1), X2) -> mark(cons(X1, X2)) 29.39/9.79 from(mark(X)) -> mark(from(X)) 29.39/9.79 s(mark(X)) -> mark(s(X)) 29.39/9.79 zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)) 29.39/9.79 zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)) 29.39/9.79 prefix(mark(X)) -> mark(prefix(X)) 29.39/9.79 proper(app(X1, X2)) -> app(proper(X1), proper(X2)) 29.39/9.79 proper(nil) -> ok(nil) 29.39/9.79 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 29.39/9.79 proper(from(X)) -> from(proper(X)) 29.39/9.79 proper(s(X)) -> s(proper(X)) 29.39/9.79 proper(zWadr(X1, X2)) -> zWadr(proper(X1), proper(X2)) 29.39/9.79 proper(prefix(X)) -> prefix(proper(X)) 29.39/9.79 app(ok(X1), ok(X2)) -> ok(app(X1, X2)) 29.39/9.79 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 29.39/9.79 from(ok(X)) -> ok(from(X)) 29.39/9.79 s(ok(X)) -> ok(s(X)) 29.39/9.79 zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)) 29.39/9.79 prefix(ok(X)) -> ok(prefix(X)) 29.39/9.79 top(mark(X)) -> top(proper(X)) 29.39/9.79 top(ok(X)) -> top(active(X)) 29.39/9.79 29.39/9.79 S is empty. 29.39/9.79 Rewrite Strategy: FULL 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 29.39/9.79 The following defined symbols can occur below the 0th argument of top: proper, active 29.39/9.79 The following defined symbols can occur below the 0th argument of proper: proper, active 29.39/9.79 The following defined symbols can occur below the 0th argument of active: proper, active 29.39/9.79 29.39/9.79 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 29.39/9.79 active(app(nil, YS)) -> mark(YS) 29.39/9.79 active(app(cons(X, XS), YS)) -> mark(cons(X, app(XS, YS))) 29.39/9.79 active(from(X)) -> mark(cons(X, from(s(X)))) 29.39/9.79 active(zWadr(nil, YS)) -> mark(nil) 29.39/9.79 active(zWadr(XS, nil)) -> mark(nil) 29.39/9.79 active(zWadr(cons(X, XS), cons(Y, YS))) -> mark(cons(app(Y, cons(X, nil)), zWadr(XS, YS))) 29.39/9.79 active(prefix(L)) -> mark(cons(nil, zWadr(L, prefix(L)))) 29.39/9.79 active(app(X1, X2)) -> app(active(X1), X2) 29.39/9.79 active(app(X1, X2)) -> app(X1, active(X2)) 29.39/9.79 active(cons(X1, X2)) -> cons(active(X1), X2) 29.39/9.79 active(from(X)) -> from(active(X)) 29.39/9.79 active(s(X)) -> s(active(X)) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(active(X1), X2) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(X1, active(X2)) 29.39/9.79 active(prefix(X)) -> prefix(active(X)) 29.39/9.79 proper(app(X1, X2)) -> app(proper(X1), proper(X2)) 29.39/9.79 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 29.39/9.79 proper(from(X)) -> from(proper(X)) 29.39/9.79 proper(s(X)) -> s(proper(X)) 29.39/9.79 proper(zWadr(X1, X2)) -> zWadr(proper(X1), proper(X2)) 29.39/9.79 proper(prefix(X)) -> prefix(proper(X)) 29.39/9.79 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (2) 29.39/9.79 Obligation: 29.39/9.79 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 29.39/9.79 29.39/9.79 29.39/9.79 The TRS R consists of the following rules: 29.39/9.79 29.39/9.79 app(mark(X1), X2) -> mark(app(X1, X2)) 29.39/9.79 app(X1, mark(X2)) -> mark(app(X1, X2)) 29.39/9.79 cons(mark(X1), X2) -> mark(cons(X1, X2)) 29.39/9.79 from(mark(X)) -> mark(from(X)) 29.39/9.79 s(mark(X)) -> mark(s(X)) 29.39/9.79 zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)) 29.39/9.79 zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)) 29.39/9.79 prefix(mark(X)) -> mark(prefix(X)) 29.39/9.79 proper(nil) -> ok(nil) 29.39/9.79 app(ok(X1), ok(X2)) -> ok(app(X1, X2)) 29.39/9.79 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 29.39/9.79 from(ok(X)) -> ok(from(X)) 29.39/9.79 s(ok(X)) -> ok(s(X)) 29.39/9.79 zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)) 29.39/9.79 prefix(ok(X)) -> ok(prefix(X)) 29.39/9.79 top(mark(X)) -> top(proper(X)) 29.39/9.79 top(ok(X)) -> top(active(X)) 29.39/9.79 29.39/9.79 S is empty. 29.39/9.79 Rewrite Strategy: FULL 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 29.39/9.79 transformed relative TRS to TRS 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (4) 29.39/9.79 Obligation: 29.39/9.79 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 29.39/9.79 29.39/9.79 29.39/9.79 The TRS R consists of the following rules: 29.39/9.79 29.39/9.79 app(mark(X1), X2) -> mark(app(X1, X2)) 29.39/9.79 app(X1, mark(X2)) -> mark(app(X1, X2)) 29.39/9.79 cons(mark(X1), X2) -> mark(cons(X1, X2)) 29.39/9.79 from(mark(X)) -> mark(from(X)) 29.39/9.79 s(mark(X)) -> mark(s(X)) 29.39/9.79 zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)) 29.39/9.79 zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)) 29.39/9.79 prefix(mark(X)) -> mark(prefix(X)) 29.39/9.79 proper(nil) -> ok(nil) 29.39/9.79 app(ok(X1), ok(X2)) -> ok(app(X1, X2)) 29.39/9.79 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 29.39/9.79 from(ok(X)) -> ok(from(X)) 29.39/9.79 s(ok(X)) -> ok(s(X)) 29.39/9.79 zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)) 29.39/9.79 prefix(ok(X)) -> ok(prefix(X)) 29.39/9.79 top(mark(X)) -> top(proper(X)) 29.39/9.79 top(ok(X)) -> top(active(X)) 29.39/9.79 29.39/9.79 S is empty. 29.39/9.79 Rewrite Strategy: FULL 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (5) CpxTrsMatchBoundsTAProof (FINISHED) 29.39/9.79 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. 29.39/9.79 29.39/9.79 The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 29.39/9.79 final states : [1, 2, 3, 4, 5, 6, 7, 8] 29.39/9.79 transitions: 29.39/9.79 mark0(0) -> 0 29.39/9.79 nil0() -> 0 29.39/9.79 ok0(0) -> 0 29.39/9.79 active0(0) -> 0 29.39/9.79 app0(0, 0) -> 1 29.39/9.79 cons0(0, 0) -> 2 29.39/9.79 from0(0) -> 3 29.39/9.79 s0(0) -> 4 29.39/9.79 zWadr0(0, 0) -> 5 29.39/9.79 prefix0(0) -> 6 29.39/9.79 proper0(0) -> 7 29.39/9.79 top0(0) -> 8 29.39/9.79 app1(0, 0) -> 9 29.39/9.79 mark1(9) -> 1 29.39/9.79 cons1(0, 0) -> 10 29.39/9.79 mark1(10) -> 2 29.39/9.79 from1(0) -> 11 29.39/9.79 mark1(11) -> 3 29.39/9.79 s1(0) -> 12 29.39/9.79 mark1(12) -> 4 29.39/9.79 zWadr1(0, 0) -> 13 29.39/9.79 mark1(13) -> 5 29.39/9.79 prefix1(0) -> 14 29.39/9.79 mark1(14) -> 6 29.39/9.79 nil1() -> 15 29.39/9.79 ok1(15) -> 7 29.39/9.79 app1(0, 0) -> 16 29.39/9.79 ok1(16) -> 1 29.39/9.79 cons1(0, 0) -> 17 29.39/9.79 ok1(17) -> 2 29.39/9.79 from1(0) -> 18 29.39/9.79 ok1(18) -> 3 29.39/9.79 s1(0) -> 19 29.39/9.79 ok1(19) -> 4 29.39/9.79 zWadr1(0, 0) -> 20 29.39/9.79 ok1(20) -> 5 29.39/9.79 prefix1(0) -> 21 29.39/9.79 ok1(21) -> 6 29.39/9.79 proper1(0) -> 22 29.39/9.79 top1(22) -> 8 29.39/9.79 active1(0) -> 23 29.39/9.79 top1(23) -> 8 29.39/9.79 mark1(9) -> 9 29.39/9.79 mark1(9) -> 16 29.39/9.79 mark1(10) -> 10 29.39/9.79 mark1(10) -> 17 29.39/9.79 mark1(11) -> 11 29.39/9.79 mark1(11) -> 18 29.39/9.79 mark1(12) -> 12 29.39/9.79 mark1(12) -> 19 29.39/9.79 mark1(13) -> 13 29.39/9.79 mark1(13) -> 20 29.39/9.79 mark1(14) -> 14 29.39/9.79 mark1(14) -> 21 29.39/9.79 ok1(15) -> 22 29.39/9.79 ok1(16) -> 9 29.39/9.79 ok1(16) -> 16 29.39/9.79 ok1(17) -> 10 29.39/9.79 ok1(17) -> 17 29.39/9.79 ok1(18) -> 11 29.39/9.79 ok1(18) -> 18 29.39/9.79 ok1(19) -> 12 29.39/9.79 ok1(19) -> 19 29.39/9.79 ok1(20) -> 13 29.39/9.79 ok1(20) -> 20 29.39/9.79 ok1(21) -> 14 29.39/9.79 ok1(21) -> 21 29.39/9.79 active2(15) -> 24 29.39/9.79 top2(24) -> 8 29.39/9.79 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (6) 29.39/9.79 BOUNDS(1, n^1) 29.39/9.79 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (7) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 29.39/9.79 Transformed a relative TRS into a decreasing-loop problem. 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (8) 29.39/9.79 Obligation: 29.39/9.79 Analyzing the following TRS for decreasing loops: 29.39/9.79 29.39/9.79 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.39/9.79 29.39/9.79 29.39/9.79 The TRS R consists of the following rules: 29.39/9.79 29.39/9.79 active(app(nil, YS)) -> mark(YS) 29.39/9.79 active(app(cons(X, XS), YS)) -> mark(cons(X, app(XS, YS))) 29.39/9.79 active(from(X)) -> mark(cons(X, from(s(X)))) 29.39/9.79 active(zWadr(nil, YS)) -> mark(nil) 29.39/9.79 active(zWadr(XS, nil)) -> mark(nil) 29.39/9.79 active(zWadr(cons(X, XS), cons(Y, YS))) -> mark(cons(app(Y, cons(X, nil)), zWadr(XS, YS))) 29.39/9.79 active(prefix(L)) -> mark(cons(nil, zWadr(L, prefix(L)))) 29.39/9.79 active(app(X1, X2)) -> app(active(X1), X2) 29.39/9.79 active(app(X1, X2)) -> app(X1, active(X2)) 29.39/9.79 active(cons(X1, X2)) -> cons(active(X1), X2) 29.39/9.79 active(from(X)) -> from(active(X)) 29.39/9.79 active(s(X)) -> s(active(X)) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(active(X1), X2) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(X1, active(X2)) 29.39/9.79 active(prefix(X)) -> prefix(active(X)) 29.39/9.79 app(mark(X1), X2) -> mark(app(X1, X2)) 29.39/9.79 app(X1, mark(X2)) -> mark(app(X1, X2)) 29.39/9.79 cons(mark(X1), X2) -> mark(cons(X1, X2)) 29.39/9.79 from(mark(X)) -> mark(from(X)) 29.39/9.79 s(mark(X)) -> mark(s(X)) 29.39/9.79 zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)) 29.39/9.79 zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)) 29.39/9.79 prefix(mark(X)) -> mark(prefix(X)) 29.39/9.79 proper(app(X1, X2)) -> app(proper(X1), proper(X2)) 29.39/9.79 proper(nil) -> ok(nil) 29.39/9.79 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 29.39/9.79 proper(from(X)) -> from(proper(X)) 29.39/9.79 proper(s(X)) -> s(proper(X)) 29.39/9.79 proper(zWadr(X1, X2)) -> zWadr(proper(X1), proper(X2)) 29.39/9.79 proper(prefix(X)) -> prefix(proper(X)) 29.39/9.79 app(ok(X1), ok(X2)) -> ok(app(X1, X2)) 29.39/9.79 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 29.39/9.79 from(ok(X)) -> ok(from(X)) 29.39/9.79 s(ok(X)) -> ok(s(X)) 29.39/9.79 zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)) 29.39/9.79 prefix(ok(X)) -> ok(prefix(X)) 29.39/9.79 top(mark(X)) -> top(proper(X)) 29.39/9.79 top(ok(X)) -> top(active(X)) 29.39/9.79 29.39/9.79 S is empty. 29.39/9.79 Rewrite Strategy: FULL 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (9) DecreasingLoopProof (LOWER BOUND(ID)) 29.39/9.79 The following loop(s) give(s) rise to the lower bound Omega(n^1): 29.39/9.79 29.39/9.79 The rewrite sequence 29.39/9.79 29.39/9.79 zWadr(mark(X1), X2) ->^+ mark(zWadr(X1, X2)) 29.39/9.79 29.39/9.79 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 29.39/9.79 29.39/9.79 The pumping substitution is [X1 / mark(X1)]. 29.39/9.79 29.39/9.79 The result substitution is [ ]. 29.39/9.79 29.39/9.79 29.39/9.79 29.39/9.79 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (10) 29.39/9.79 Complex Obligation (BEST) 29.39/9.79 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (11) 29.39/9.79 Obligation: 29.39/9.79 Proved the lower bound n^1 for the following obligation: 29.39/9.79 29.39/9.79 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.39/9.79 29.39/9.79 29.39/9.79 The TRS R consists of the following rules: 29.39/9.79 29.39/9.79 active(app(nil, YS)) -> mark(YS) 29.39/9.79 active(app(cons(X, XS), YS)) -> mark(cons(X, app(XS, YS))) 29.39/9.79 active(from(X)) -> mark(cons(X, from(s(X)))) 29.39/9.79 active(zWadr(nil, YS)) -> mark(nil) 29.39/9.79 active(zWadr(XS, nil)) -> mark(nil) 29.39/9.79 active(zWadr(cons(X, XS), cons(Y, YS))) -> mark(cons(app(Y, cons(X, nil)), zWadr(XS, YS))) 29.39/9.79 active(prefix(L)) -> mark(cons(nil, zWadr(L, prefix(L)))) 29.39/9.79 active(app(X1, X2)) -> app(active(X1), X2) 29.39/9.79 active(app(X1, X2)) -> app(X1, active(X2)) 29.39/9.79 active(cons(X1, X2)) -> cons(active(X1), X2) 29.39/9.79 active(from(X)) -> from(active(X)) 29.39/9.79 active(s(X)) -> s(active(X)) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(active(X1), X2) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(X1, active(X2)) 29.39/9.79 active(prefix(X)) -> prefix(active(X)) 29.39/9.79 app(mark(X1), X2) -> mark(app(X1, X2)) 29.39/9.79 app(X1, mark(X2)) -> mark(app(X1, X2)) 29.39/9.79 cons(mark(X1), X2) -> mark(cons(X1, X2)) 29.39/9.79 from(mark(X)) -> mark(from(X)) 29.39/9.79 s(mark(X)) -> mark(s(X)) 29.39/9.79 zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)) 29.39/9.79 zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)) 29.39/9.79 prefix(mark(X)) -> mark(prefix(X)) 29.39/9.79 proper(app(X1, X2)) -> app(proper(X1), proper(X2)) 29.39/9.79 proper(nil) -> ok(nil) 29.39/9.79 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 29.39/9.79 proper(from(X)) -> from(proper(X)) 29.39/9.79 proper(s(X)) -> s(proper(X)) 29.39/9.79 proper(zWadr(X1, X2)) -> zWadr(proper(X1), proper(X2)) 29.39/9.79 proper(prefix(X)) -> prefix(proper(X)) 29.39/9.79 app(ok(X1), ok(X2)) -> ok(app(X1, X2)) 29.39/9.79 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 29.39/9.79 from(ok(X)) -> ok(from(X)) 29.39/9.79 s(ok(X)) -> ok(s(X)) 29.39/9.79 zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)) 29.39/9.79 prefix(ok(X)) -> ok(prefix(X)) 29.39/9.79 top(mark(X)) -> top(proper(X)) 29.39/9.79 top(ok(X)) -> top(active(X)) 29.39/9.79 29.39/9.79 S is empty. 29.39/9.79 Rewrite Strategy: FULL 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (12) LowerBoundPropagationProof (FINISHED) 29.39/9.79 Propagated lower bound. 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (13) 29.39/9.79 BOUNDS(n^1, INF) 29.39/9.79 29.39/9.79 ---------------------------------------- 29.39/9.79 29.39/9.79 (14) 29.39/9.79 Obligation: 29.39/9.79 Analyzing the following TRS for decreasing loops: 29.39/9.79 29.39/9.79 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.39/9.79 29.39/9.79 29.39/9.79 The TRS R consists of the following rules: 29.39/9.79 29.39/9.79 active(app(nil, YS)) -> mark(YS) 29.39/9.79 active(app(cons(X, XS), YS)) -> mark(cons(X, app(XS, YS))) 29.39/9.79 active(from(X)) -> mark(cons(X, from(s(X)))) 29.39/9.79 active(zWadr(nil, YS)) -> mark(nil) 29.39/9.79 active(zWadr(XS, nil)) -> mark(nil) 29.39/9.79 active(zWadr(cons(X, XS), cons(Y, YS))) -> mark(cons(app(Y, cons(X, nil)), zWadr(XS, YS))) 29.39/9.79 active(prefix(L)) -> mark(cons(nil, zWadr(L, prefix(L)))) 29.39/9.79 active(app(X1, X2)) -> app(active(X1), X2) 29.39/9.79 active(app(X1, X2)) -> app(X1, active(X2)) 29.39/9.79 active(cons(X1, X2)) -> cons(active(X1), X2) 29.39/9.79 active(from(X)) -> from(active(X)) 29.39/9.79 active(s(X)) -> s(active(X)) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(active(X1), X2) 29.39/9.79 active(zWadr(X1, X2)) -> zWadr(X1, active(X2)) 29.39/9.79 active(prefix(X)) -> prefix(active(X)) 29.39/9.79 app(mark(X1), X2) -> mark(app(X1, X2)) 29.39/9.79 app(X1, mark(X2)) -> mark(app(X1, X2)) 29.39/9.79 cons(mark(X1), X2) -> mark(cons(X1, X2)) 29.39/9.79 from(mark(X)) -> mark(from(X)) 29.39/9.79 s(mark(X)) -> mark(s(X)) 29.39/9.79 zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)) 29.39/9.79 zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)) 29.39/9.79 prefix(mark(X)) -> mark(prefix(X)) 29.39/9.79 proper(app(X1, X2)) -> app(proper(X1), proper(X2)) 29.39/9.79 proper(nil) -> ok(nil) 29.39/9.79 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 29.39/9.79 proper(from(X)) -> from(proper(X)) 29.39/9.79 proper(s(X)) -> s(proper(X)) 29.39/9.79 proper(zWadr(X1, X2)) -> zWadr(proper(X1), proper(X2)) 29.39/9.79 proper(prefix(X)) -> prefix(proper(X)) 29.39/9.79 app(ok(X1), ok(X2)) -> ok(app(X1, X2)) 29.39/9.79 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 29.39/9.79 from(ok(X)) -> ok(from(X)) 29.39/9.79 s(ok(X)) -> ok(s(X)) 29.39/9.79 zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)) 29.39/9.79 prefix(ok(X)) -> ok(prefix(X)) 29.39/9.79 top(mark(X)) -> top(proper(X)) 29.39/9.79 top(ok(X)) -> top(active(X)) 29.39/9.79 29.39/9.79 S is empty. 29.39/9.79 Rewrite Strategy: FULL 29.59/9.83 EOF