0.00/0.07 YES 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 0.00/0.07 (VAR v_NonEmpty:S X:S) 0.00/0.07 (RULES 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ) 0.00/0.07 (STRATEGY INNERMOST) 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 0.00/0.07 Dependency Pairs Processor: 0.00/0.07 -> Pairs: 0.00/0.07 ACTIVE(f(X:S)) -> ACTIVE(X:S) 0.00/0.07 ACTIVE(f(X:S)) -> F(active(X:S)) 0.00/0.07 ACTIVE(g(X:S)) -> ACTIVE(X:S) 0.00/0.07 ACTIVE(g(X:S)) -> G(active(X:S)) 0.00/0.07 C(ok(X:S)) -> C(X:S) 0.00/0.07 F(mark(X:S)) -> F(X:S) 0.00/0.07 F(ok(X:S)) -> F(X:S) 0.00/0.07 G(mark(X:S)) -> G(X:S) 0.00/0.07 G(ok(X:S)) -> G(X:S) 0.00/0.07 PROPER(c(X:S)) -> C(proper(X:S)) 0.00/0.07 PROPER(c(X:S)) -> PROPER(X:S) 0.00/0.07 PROPER(f(X:S)) -> F(proper(X:S)) 0.00/0.07 PROPER(f(X:S)) -> PROPER(X:S) 0.00/0.07 PROPER(g(X:S)) -> G(proper(X:S)) 0.00/0.07 PROPER(g(X:S)) -> PROPER(X:S) 0.00/0.07 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.07 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.07 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.07 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 0.00/0.07 Problem 1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 ACTIVE(f(X:S)) -> ACTIVE(X:S) 0.00/0.07 ACTIVE(f(X:S)) -> F(active(X:S)) 0.00/0.07 ACTIVE(g(X:S)) -> ACTIVE(X:S) 0.00/0.07 ACTIVE(g(X:S)) -> G(active(X:S)) 0.00/0.07 C(ok(X:S)) -> C(X:S) 0.00/0.07 F(mark(X:S)) -> F(X:S) 0.00/0.07 F(ok(X:S)) -> F(X:S) 0.00/0.07 G(mark(X:S)) -> G(X:S) 0.00/0.07 G(ok(X:S)) -> G(X:S) 0.00/0.07 PROPER(c(X:S)) -> C(proper(X:S)) 0.00/0.07 PROPER(c(X:S)) -> PROPER(X:S) 0.00/0.07 PROPER(f(X:S)) -> F(proper(X:S)) 0.00/0.07 PROPER(f(X:S)) -> PROPER(X:S) 0.00/0.07 PROPER(g(X:S)) -> G(proper(X:S)) 0.00/0.07 PROPER(g(X:S)) -> PROPER(X:S) 0.00/0.07 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.07 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.07 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.07 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 G(mark(X:S)) -> G(X:S) 0.00/0.07 G(ok(X:S)) -> G(X:S) 0.00/0.07 ->->-> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 F(mark(X:S)) -> F(X:S) 0.00/0.07 F(ok(X:S)) -> F(X:S) 0.00/0.07 ->->-> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 C(ok(X:S)) -> C(X:S) 0.00/0.07 ->->-> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 PROPER(c(X:S)) -> PROPER(X:S) 0.00/0.07 PROPER(f(X:S)) -> PROPER(X:S) 0.00/0.07 PROPER(g(X:S)) -> PROPER(X:S) 0.00/0.07 ->->-> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 ACTIVE(f(X:S)) -> ACTIVE(X:S) 0.00/0.07 ACTIVE(g(X:S)) -> ACTIVE(X:S) 0.00/0.07 ->->-> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.07 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.07 ->->-> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 0.00/0.07 0.00/0.07 The problem is decomposed in 6 subproblems. 0.00/0.07 0.00/0.07 Problem 1.1: 0.00/0.07 0.00/0.07 Subterm Processor: 0.00/0.07 -> Pairs: 0.00/0.07 G(mark(X:S)) -> G(X:S) 0.00/0.07 G(ok(X:S)) -> G(X:S) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Projection: 0.00/0.07 pi(G) = 1 0.00/0.07 0.00/0.07 Problem 1.1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 0.00/0.07 Problem 1.2: 0.00/0.07 0.00/0.07 Subterm Processor: 0.00/0.07 -> Pairs: 0.00/0.07 F(mark(X:S)) -> F(X:S) 0.00/0.07 F(ok(X:S)) -> F(X:S) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Projection: 0.00/0.07 pi(F) = 1 0.00/0.07 0.00/0.07 Problem 1.2: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 0.00/0.07 Problem 1.3: 0.00/0.07 0.00/0.07 Subterm Processor: 0.00/0.07 -> Pairs: 0.00/0.07 C(ok(X:S)) -> C(X:S) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Projection: 0.00/0.07 pi(C) = 1 0.00/0.07 0.00/0.07 Problem 1.3: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 0.00/0.07 Problem 1.4: 0.00/0.07 0.00/0.07 Subterm Processor: 0.00/0.07 -> Pairs: 0.00/0.07 PROPER(c(X:S)) -> PROPER(X:S) 0.00/0.07 PROPER(f(X:S)) -> PROPER(X:S) 0.00/0.07 PROPER(g(X:S)) -> PROPER(X:S) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Projection: 0.00/0.07 pi(PROPER) = 1 0.00/0.07 0.00/0.07 Problem 1.4: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 0.00/0.07 Problem 1.5: 0.00/0.07 0.00/0.07 Subterm Processor: 0.00/0.07 -> Pairs: 0.00/0.07 ACTIVE(f(X:S)) -> ACTIVE(X:S) 0.00/0.07 ACTIVE(g(X:S)) -> ACTIVE(X:S) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Projection: 0.00/0.07 pi(ACTIVE) = 1 0.00/0.07 0.00/0.07 Problem 1.5: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 0.00/0.07 Problem 1.6: 0.00/0.07 0.00/0.07 Reduction Pairs Processor: 0.00/0.07 -> Pairs: 0.00/0.07 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.07 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 -> Usable rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 ->Interpretation type: 0.00/0.07 Linear 0.00/0.07 ->Coefficients: 0.00/0.07 Natural Numbers 0.00/0.07 ->Dimension: 0.00/0.07 1 0.00/0.07 ->Bound: 0.00/0.07 2 0.00/0.07 ->Interpretation: 0.00/0.07 0.00/0.07 [active](X) = X 0.00/0.07 [c](X) = 0 0.00/0.07 [f](X) = 2.X + 2 0.00/0.07 [g](X) = 2.X + 2 0.00/0.07 [proper](X) = 2.X 0.00/0.07 [top](X) = 0 0.00/0.07 [a] = 2 0.00/0.07 [fSNonEmpty] = 0 0.00/0.07 [mark](X) = 2.X + 2 0.00/0.07 [ok](X) = X 0.00/0.07 [ACTIVE](X) = 0 0.00/0.07 [C](X) = 0 0.00/0.07 [F](X) = 0 0.00/0.07 [G](X) = 0 0.00/0.07 [PROPER](X) = 0 0.00/0.07 [TOP](X) = 2.X 0.00/0.07 0.00/0.07 Problem 1.6: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 ->->Cycle: 0.00/0.07 ->->-> Pairs: 0.00/0.07 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.07 ->->-> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 0.00/0.07 Problem 1.6: 0.00/0.07 0.00/0.07 Reduction Pairs Processor: 0.00/0.07 -> Pairs: 0.00/0.07 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 -> Usable rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 ->Interpretation type: 0.00/0.07 Linear 0.00/0.07 ->Coefficients: 0.00/0.07 Natural Numbers 0.00/0.07 ->Dimension: 0.00/0.07 1 0.00/0.07 ->Bound: 0.00/0.07 2 0.00/0.07 ->Interpretation: 0.00/0.07 0.00/0.07 [active](X) = 2.X + 1 0.00/0.07 [c](X) = 2.X + 2 0.00/0.07 [f](X) = 2.X + 2 0.00/0.07 [g](X) = 2.X + 2 0.00/0.07 [proper](X) = 0 0.00/0.07 [top](X) = 0 0.00/0.07 [a] = 0 0.00/0.07 [fSNonEmpty] = 0 0.00/0.07 [mark](X) = 1 0.00/0.07 [ok](X) = 2.X + 2 0.00/0.07 [ACTIVE](X) = 0 0.00/0.07 [C](X) = 0 0.00/0.07 [F](X) = 0 0.00/0.07 [G](X) = 0 0.00/0.07 [PROPER](X) = 0 0.00/0.07 [TOP](X) = 2.X 0.00/0.07 0.00/0.07 Problem 1.6: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 active(f(f(a))) -> mark(c(f(g(f(a))))) 0.00/0.07 active(f(X:S)) -> f(active(X:S)) 0.00/0.07 active(g(X:S)) -> g(active(X:S)) 0.00/0.07 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.07 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.07 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.07 g(mark(X:S)) -> mark(g(X:S)) 0.00/0.07 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.07 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.07 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.07 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.07 proper(a) -> ok(a) 0.00/0.07 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.07 top(ok(X:S)) -> top(active(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 EOF