0.00/0.10 YES 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 (VAR v_NonEmpty:S X:S) 0.00/0.10 (RULES 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ) 0.00/0.10 (STRATEGY INNERMOST) 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 Dependency Pairs Processor: 0.00/0.10 -> Pairs: 0.00/0.10 ACTIVE(c(X:S)) -> D(X:S) 0.00/0.10 ACTIVE(f(f(X:S))) -> C(f(g(f(X:S)))) 0.00/0.10 ACTIVE(f(f(X:S))) -> F(g(f(X:S))) 0.00/0.10 ACTIVE(f(f(X:S))) -> G(f(X:S)) 0.00/0.10 ACTIVE(f(X:S)) -> ACTIVE(X:S) 0.00/0.10 ACTIVE(f(X:S)) -> F(active(X:S)) 0.00/0.10 ACTIVE(h(X:S)) -> ACTIVE(X:S) 0.00/0.10 ACTIVE(h(X:S)) -> C(d(X:S)) 0.00/0.10 ACTIVE(h(X:S)) -> D(X:S) 0.00/0.10 ACTIVE(h(X:S)) -> H(active(X:S)) 0.00/0.10 C(ok(X:S)) -> C(X:S) 0.00/0.10 D(ok(X:S)) -> D(X:S) 0.00/0.10 F(mark(X:S)) -> F(X:S) 0.00/0.10 F(ok(X:S)) -> F(X:S) 0.00/0.10 G(ok(X:S)) -> G(X:S) 0.00/0.10 H(mark(X:S)) -> H(X:S) 0.00/0.10 H(ok(X:S)) -> H(X:S) 0.00/0.10 PROPER(c(X:S)) -> C(proper(X:S)) 0.00/0.10 PROPER(c(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(d(X:S)) -> D(proper(X:S)) 0.00/0.10 PROPER(d(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(f(X:S)) -> F(proper(X:S)) 0.00/0.10 PROPER(f(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(g(X:S)) -> G(proper(X:S)) 0.00/0.10 PROPER(g(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(h(X:S)) -> H(proper(X:S)) 0.00/0.10 PROPER(h(X:S)) -> PROPER(X:S) 0.00/0.10 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.10 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.10 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 ACTIVE(c(X:S)) -> D(X:S) 0.00/0.10 ACTIVE(f(f(X:S))) -> C(f(g(f(X:S)))) 0.00/0.10 ACTIVE(f(f(X:S))) -> F(g(f(X:S))) 0.00/0.10 ACTIVE(f(f(X:S))) -> G(f(X:S)) 0.00/0.10 ACTIVE(f(X:S)) -> ACTIVE(X:S) 0.00/0.10 ACTIVE(f(X:S)) -> F(active(X:S)) 0.00/0.10 ACTIVE(h(X:S)) -> ACTIVE(X:S) 0.00/0.10 ACTIVE(h(X:S)) -> C(d(X:S)) 0.00/0.10 ACTIVE(h(X:S)) -> D(X:S) 0.00/0.10 ACTIVE(h(X:S)) -> H(active(X:S)) 0.00/0.10 C(ok(X:S)) -> C(X:S) 0.00/0.10 D(ok(X:S)) -> D(X:S) 0.00/0.10 F(mark(X:S)) -> F(X:S) 0.00/0.10 F(ok(X:S)) -> F(X:S) 0.00/0.10 G(ok(X:S)) -> G(X:S) 0.00/0.10 H(mark(X:S)) -> H(X:S) 0.00/0.10 H(ok(X:S)) -> H(X:S) 0.00/0.10 PROPER(c(X:S)) -> C(proper(X:S)) 0.00/0.10 PROPER(c(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(d(X:S)) -> D(proper(X:S)) 0.00/0.10 PROPER(d(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(f(X:S)) -> F(proper(X:S)) 0.00/0.10 PROPER(f(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(g(X:S)) -> G(proper(X:S)) 0.00/0.10 PROPER(g(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(h(X:S)) -> H(proper(X:S)) 0.00/0.10 PROPER(h(X:S)) -> PROPER(X:S) 0.00/0.10 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.10 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.10 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 H(mark(X:S)) -> H(X:S) 0.00/0.10 H(ok(X:S)) -> H(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 G(ok(X:S)) -> G(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 F(mark(X:S)) -> F(X:S) 0.00/0.10 F(ok(X:S)) -> F(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 D(ok(X:S)) -> D(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 C(ok(X:S)) -> C(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 PROPER(c(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(d(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(f(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(g(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(h(X:S)) -> PROPER(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 ACTIVE(f(X:S)) -> ACTIVE(X:S) 0.00/0.10 ACTIVE(h(X:S)) -> ACTIVE(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.10 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.10 ->->-> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 0.00/0.10 0.00/0.10 The problem is decomposed in 8 subproblems. 0.00/0.10 0.00/0.10 Problem 1.1: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 H(mark(X:S)) -> H(X:S) 0.00/0.10 H(ok(X:S)) -> H(X:S) 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(H) = 1 0.00/0.10 0.00/0.10 Problem 1.1: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.2: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 G(ok(X:S)) -> G(X:S) 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(G) = 1 0.00/0.10 0.00/0.10 Problem 1.2: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.3: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 F(mark(X:S)) -> F(X:S) 0.00/0.10 F(ok(X:S)) -> F(X:S) 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(F) = 1 0.00/0.10 0.00/0.10 Problem 1.3: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.4: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 D(ok(X:S)) -> D(X:S) 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(D) = 1 0.00/0.10 0.00/0.10 Problem 1.4: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.5: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 C(ok(X:S)) -> C(X:S) 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(C) = 1 0.00/0.10 0.00/0.10 Problem 1.5: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 0.00/0.10 Problem 1.6: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 PROPER(c(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(d(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(f(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(g(X:S)) -> PROPER(X:S) 0.00/0.10 PROPER(h(X:S)) -> PROPER(X:S) 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.10 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.10 top(ok(X:S)) -> top(active(X:S)) 0.00/0.10 ->Projection: 0.00/0.10 pi(PROPER) = 1 0.00/0.10 0.00/0.10 Problem 1.6: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 active(c(X:S)) -> mark(d(X:S)) 0.00/0.10 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.10 active(f(X:S)) -> f(active(X:S)) 0.00/0.10 active(h(X:S)) -> h(active(X:S)) 0.00/0.10 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.10 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.10 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.10 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.10 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.10 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.10 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.10 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.10 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.10 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.10 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.10 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.10 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.11 top(ok(X:S)) -> top(active(X:S)) 0.00/0.11 ->Strongly Connected Components: 0.00/0.11 There is no strongly connected component 0.00/0.11 0.00/0.11 The problem is finite. 0.00/0.11 0.00/0.11 Problem 1.7: 0.00/0.11 0.00/0.11 Subterm Processor: 0.00/0.11 -> Pairs: 0.00/0.11 ACTIVE(f(X:S)) -> ACTIVE(X:S) 0.00/0.11 ACTIVE(h(X:S)) -> ACTIVE(X:S) 0.00/0.11 -> Rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.11 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.11 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.11 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.11 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.11 top(ok(X:S)) -> top(active(X:S)) 0.00/0.11 ->Projection: 0.00/0.11 pi(ACTIVE) = 1 0.00/0.11 0.00/0.11 Problem 1.7: 0.00/0.11 0.00/0.11 SCC Processor: 0.00/0.11 -> Pairs: 0.00/0.11 Empty 0.00/0.11 -> Rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.11 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.11 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.11 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.11 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.11 top(ok(X:S)) -> top(active(X:S)) 0.00/0.11 ->Strongly Connected Components: 0.00/0.11 There is no strongly connected component 0.00/0.11 0.00/0.11 The problem is finite. 0.00/0.11 0.00/0.11 Problem 1.8: 0.00/0.11 0.00/0.11 Reduction Pairs Processor: 0.00/0.11 -> Pairs: 0.00/0.11 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.11 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.11 -> Rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.11 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.11 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.11 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.11 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.11 top(ok(X:S)) -> top(active(X:S)) 0.00/0.11 -> Usable rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.11 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.11 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.11 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.11 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 ->Interpretation type: 0.00/0.11 Linear 0.00/0.11 ->Coefficients: 0.00/0.11 Natural Numbers 0.00/0.11 ->Dimension: 0.00/0.11 1 0.00/0.11 ->Bound: 0.00/0.11 2 0.00/0.11 ->Interpretation: 0.00/0.11 0.00/0.11 [active](X) = X 0.00/0.11 [c](X) = 1 0.00/0.11 [d](X) = 0 0.00/0.11 [f](X) = 2.X + 2 0.00/0.11 [g](X) = 2 0.00/0.11 [h](X) = 2.X + 2 0.00/0.11 [proper](X) = X 0.00/0.11 [top](X) = 0 0.00/0.11 [fSNonEmpty] = 0 0.00/0.11 [mark](X) = X + 1 0.00/0.11 [ok](X) = X 0.00/0.11 [ACTIVE](X) = 0 0.00/0.11 [C](X) = 0 0.00/0.11 [D](X) = 0 0.00/0.11 [F](X) = 0 0.00/0.11 [G](X) = 0 0.00/0.11 [H](X) = 0 0.00/0.11 [PROPER](X) = 0 0.00/0.11 [TOP](X) = 2.X 0.00/0.11 0.00/0.11 Problem 1.8: 0.00/0.11 0.00/0.11 SCC Processor: 0.00/0.11 -> Pairs: 0.00/0.11 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.11 -> Rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.11 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.11 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.11 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.11 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.11 top(ok(X:S)) -> top(active(X:S)) 0.00/0.11 ->Strongly Connected Components: 0.00/0.11 ->->Cycle: 0.00/0.11 ->->-> Pairs: 0.00/0.11 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.11 ->->-> Rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.11 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.11 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.11 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.11 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.11 top(ok(X:S)) -> top(active(X:S)) 0.00/0.11 0.00/0.11 Problem 1.8: 0.00/0.11 0.00/0.11 Reduction Pairs Processor: 0.00/0.11 -> Pairs: 0.00/0.11 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.11 -> Rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.11 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.11 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.11 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.11 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.11 top(ok(X:S)) -> top(active(X:S)) 0.00/0.11 -> Usable rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 ->Interpretation type: 0.00/0.11 Linear 0.00/0.11 ->Coefficients: 0.00/0.11 Natural Numbers 0.00/0.11 ->Dimension: 0.00/0.11 1 0.00/0.11 ->Bound: 0.00/0.11 2 0.00/0.11 ->Interpretation: 0.00/0.11 0.00/0.11 [active](X) = 2.X + 1 0.00/0.11 [c](X) = 2.X + 1 0.00/0.11 [d](X) = 2.X + 2 0.00/0.11 [f](X) = 2.X + 2 0.00/0.11 [g](X) = X 0.00/0.11 [h](X) = 2.X + 2 0.00/0.11 [proper](X) = 0 0.00/0.11 [top](X) = 0 0.00/0.11 [fSNonEmpty] = 0 0.00/0.11 [mark](X) = X 0.00/0.11 [ok](X) = 2.X + 2 0.00/0.11 [ACTIVE](X) = 0 0.00/0.11 [C](X) = 0 0.00/0.11 [D](X) = 0 0.00/0.11 [F](X) = 0 0.00/0.11 [G](X) = 0 0.00/0.11 [H](X) = 0 0.00/0.11 [PROPER](X) = 0 0.00/0.11 [TOP](X) = X 0.00/0.11 0.00/0.11 Problem 1.8: 0.00/0.11 0.00/0.11 SCC Processor: 0.00/0.11 -> Pairs: 0.00/0.11 Empty 0.00/0.11 -> Rules: 0.00/0.11 active(c(X:S)) -> mark(d(X:S)) 0.00/0.11 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.11 active(f(X:S)) -> f(active(X:S)) 0.00/0.11 active(h(X:S)) -> h(active(X:S)) 0.00/0.11 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.11 c(ok(X:S)) -> ok(c(X:S)) 0.00/0.11 d(ok(X:S)) -> ok(d(X:S)) 0.00/0.11 f(mark(X:S)) -> mark(f(X:S)) 0.00/0.11 f(ok(X:S)) -> ok(f(X:S)) 0.00/0.11 g(ok(X:S)) -> ok(g(X:S)) 0.00/0.11 h(mark(X:S)) -> mark(h(X:S)) 0.00/0.11 h(ok(X:S)) -> ok(h(X:S)) 0.00/0.11 proper(c(X:S)) -> c(proper(X:S)) 0.00/0.11 proper(d(X:S)) -> d(proper(X:S)) 0.00/0.11 proper(f(X:S)) -> f(proper(X:S)) 0.00/0.11 proper(g(X:S)) -> g(proper(X:S)) 0.00/0.11 proper(h(X:S)) -> h(proper(X:S)) 0.00/0.11 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.11 top(ok(X:S)) -> top(active(X:S)) 0.00/0.11 ->Strongly Connected Components: 0.00/0.11 There is no strongly connected component 0.00/0.11 0.00/0.11 The problem is finite. 0.00/0.11 EOF