0.00/0.09 YES 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 (VAR v_NonEmpty:S X:S) 0.00/0.09 (RULES 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ) 0.00/0.09 (STRATEGY INNERMOST) 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 Dependency Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 ACTIVE(c(X:S)) -> D(X:S) 0.00/0.09 ACTIVE(c(X:S)) -> MARK(d(X:S)) 0.00/0.09 ACTIVE(f(f(X:S))) -> C(f(g(f(X:S)))) 0.00/0.09 ACTIVE(f(f(X:S))) -> F(g(f(X:S))) 0.00/0.09 ACTIVE(f(f(X:S))) -> G(f(X:S)) 0.00/0.09 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S))))) 0.00/0.09 ACTIVE(h(X:S)) -> C(d(X:S)) 0.00/0.09 ACTIVE(h(X:S)) -> D(X:S) 0.00/0.09 ACTIVE(h(X:S)) -> MARK(c(d(X:S))) 0.00/0.09 C(active(X:S)) -> C(X:S) 0.00/0.09 C(mark(X:S)) -> C(X:S) 0.00/0.09 D(active(X:S)) -> D(X:S) 0.00/0.09 D(mark(X:S)) -> D(X:S) 0.00/0.09 F(active(X:S)) -> F(X:S) 0.00/0.09 F(mark(X:S)) -> F(X:S) 0.00/0.09 G(active(X:S)) -> G(X:S) 0.00/0.09 G(mark(X:S)) -> G(X:S) 0.00/0.09 H(active(X:S)) -> H(X:S) 0.00/0.09 H(mark(X:S)) -> H(X:S) 0.00/0.09 MARK(c(X:S)) -> ACTIVE(c(X:S)) 0.00/0.09 MARK(d(X:S)) -> ACTIVE(d(X:S)) 0.00/0.09 MARK(f(X:S)) -> ACTIVE(f(mark(X:S))) 0.00/0.09 MARK(f(X:S)) -> F(mark(X:S)) 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(g(X:S)) -> ACTIVE(g(X:S)) 0.00/0.09 MARK(h(X:S)) -> ACTIVE(h(mark(X:S))) 0.00/0.09 MARK(h(X:S)) -> H(mark(X:S)) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 ACTIVE(c(X:S)) -> D(X:S) 0.00/0.09 ACTIVE(c(X:S)) -> MARK(d(X:S)) 0.00/0.09 ACTIVE(f(f(X:S))) -> C(f(g(f(X:S)))) 0.00/0.09 ACTIVE(f(f(X:S))) -> F(g(f(X:S))) 0.00/0.09 ACTIVE(f(f(X:S))) -> G(f(X:S)) 0.00/0.09 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S))))) 0.00/0.09 ACTIVE(h(X:S)) -> C(d(X:S)) 0.00/0.09 ACTIVE(h(X:S)) -> D(X:S) 0.00/0.09 ACTIVE(h(X:S)) -> MARK(c(d(X:S))) 0.00/0.09 C(active(X:S)) -> C(X:S) 0.00/0.09 C(mark(X:S)) -> C(X:S) 0.00/0.09 D(active(X:S)) -> D(X:S) 0.00/0.09 D(mark(X:S)) -> D(X:S) 0.00/0.09 F(active(X:S)) -> F(X:S) 0.00/0.09 F(mark(X:S)) -> F(X:S) 0.00/0.09 G(active(X:S)) -> G(X:S) 0.00/0.09 G(mark(X:S)) -> G(X:S) 0.00/0.09 H(active(X:S)) -> H(X:S) 0.00/0.09 H(mark(X:S)) -> H(X:S) 0.00/0.09 MARK(c(X:S)) -> ACTIVE(c(X:S)) 0.00/0.09 MARK(d(X:S)) -> ACTIVE(d(X:S)) 0.00/0.09 MARK(f(X:S)) -> ACTIVE(f(mark(X:S))) 0.00/0.09 MARK(f(X:S)) -> F(mark(X:S)) 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(g(X:S)) -> ACTIVE(g(X:S)) 0.00/0.09 MARK(h(X:S)) -> ACTIVE(h(mark(X:S))) 0.00/0.09 MARK(h(X:S)) -> H(mark(X:S)) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 H(active(X:S)) -> H(X:S) 0.00/0.09 H(mark(X:S)) -> H(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 G(active(X:S)) -> G(X:S) 0.00/0.09 G(mark(X:S)) -> G(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 F(active(X:S)) -> F(X:S) 0.00/0.09 F(mark(X:S)) -> F(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 D(active(X:S)) -> D(X:S) 0.00/0.09 D(mark(X:S)) -> D(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 C(active(X:S)) -> C(X:S) 0.00/0.09 C(mark(X:S)) -> C(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 ACTIVE(c(X:S)) -> MARK(d(X:S)) 0.00/0.09 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S))))) 0.00/0.09 ACTIVE(h(X:S)) -> MARK(c(d(X:S))) 0.00/0.09 MARK(c(X:S)) -> ACTIVE(c(X:S)) 0.00/0.09 MARK(f(X:S)) -> ACTIVE(f(mark(X:S))) 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(h(X:S)) -> ACTIVE(h(mark(X:S))) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 0.00/0.09 0.00/0.09 The problem is decomposed in 6 subproblems. 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 H(active(X:S)) -> H(X:S) 0.00/0.09 H(mark(X:S)) -> H(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Projection: 0.00/0.09 pi(H) = 1 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.2: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 G(active(X:S)) -> G(X:S) 0.00/0.09 G(mark(X:S)) -> G(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Projection: 0.00/0.09 pi(G) = 1 0.00/0.09 0.00/0.09 Problem 1.2: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.3: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 F(active(X:S)) -> F(X:S) 0.00/0.09 F(mark(X:S)) -> F(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Projection: 0.00/0.09 pi(F) = 1 0.00/0.09 0.00/0.09 Problem 1.3: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.4: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 D(active(X:S)) -> D(X:S) 0.00/0.09 D(mark(X:S)) -> D(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Projection: 0.00/0.09 pi(D) = 1 0.00/0.09 0.00/0.09 Problem 1.4: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.5: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 C(active(X:S)) -> C(X:S) 0.00/0.09 C(mark(X:S)) -> C(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Projection: 0.00/0.09 pi(C) = 1 0.00/0.09 0.00/0.09 Problem 1.5: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 ACTIVE(c(X:S)) -> MARK(d(X:S)) 0.00/0.09 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S))))) 0.00/0.09 ACTIVE(h(X:S)) -> MARK(c(d(X:S))) 0.00/0.09 MARK(c(X:S)) -> ACTIVE(c(X:S)) 0.00/0.09 MARK(f(X:S)) -> ACTIVE(f(mark(X:S))) 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(h(X:S)) -> ACTIVE(h(mark(X:S))) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 -> Usable rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [active](X) = X 0.00/0.09 [c](X) = 2 0.00/0.09 [d](X) = 0 0.00/0.09 [f](X) = 2.X + 1 0.00/0.09 [g](X) = 2.X + 2 0.00/0.09 [h](X) = 2.X + 2 0.00/0.09 [mark](X) = X 0.00/0.09 [fSNonEmpty] = 0 0.00/0.09 [ACTIVE](X) = 2.X 0.00/0.09 [C](X) = 0 0.00/0.09 [D](X) = 0 0.00/0.09 [F](X) = 0 0.00/0.09 [G](X) = 0 0.00/0.09 [H](X) = 0 0.00/0.09 [MARK](X) = 2.X 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S))))) 0.00/0.09 ACTIVE(h(X:S)) -> MARK(c(d(X:S))) 0.00/0.09 MARK(c(X:S)) -> ACTIVE(c(X:S)) 0.00/0.09 MARK(f(X:S)) -> ACTIVE(f(mark(X:S))) 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(h(X:S)) -> ACTIVE(h(mark(X:S))) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 ACTIVE(h(X:S)) -> MARK(c(d(X:S))) 0.00/0.09 MARK(f(X:S)) -> ACTIVE(f(mark(X:S))) 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(h(X:S)) -> ACTIVE(h(mark(X:S))) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 ACTIVE(h(X:S)) -> MARK(c(d(X:S))) 0.00/0.09 MARK(f(X:S)) -> ACTIVE(f(mark(X:S))) 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(h(X:S)) -> ACTIVE(h(mark(X:S))) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 -> Usable rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [active](X) = X 0.00/0.09 [c](X) = 0 0.00/0.09 [d](X) = 0 0.00/0.09 [f](X) = 2.X 0.00/0.09 [g](X) = 0 0.00/0.09 [h](X) = 2.X + 2 0.00/0.09 [mark](X) = 2.X 0.00/0.09 [fSNonEmpty] = 0 0.00/0.09 [ACTIVE](X) = X 0.00/0.09 [C](X) = 0 0.00/0.09 [D](X) = 0 0.00/0.09 [F](X) = 0 0.00/0.09 [G](X) = 0 0.00/0.09 [H](X) = 0 0.00/0.09 [MARK](X) = 2.X + 1 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 MARK(f(X:S)) -> ACTIVE(f(mark(X:S))) 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(h(X:S)) -> ACTIVE(h(mark(X:S))) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 Subterm Processor: 0.00/0.09 -> Pairs: 0.00/0.09 MARK(f(X:S)) -> MARK(X:S) 0.00/0.09 MARK(h(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Projection: 0.00/0.09 pi(MARK) = 1 0.00/0.09 0.00/0.09 Problem 1.6: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 active(c(X:S)) -> mark(d(X:S)) 0.00/0.09 active(f(f(X:S))) -> mark(c(f(g(f(X:S))))) 0.00/0.09 active(h(X:S)) -> mark(c(d(X:S))) 0.00/0.09 c(active(X:S)) -> c(X:S) 0.00/0.09 c(mark(X:S)) -> c(X:S) 0.00/0.09 d(active(X:S)) -> d(X:S) 0.00/0.09 d(mark(X:S)) -> d(X:S) 0.00/0.09 f(active(X:S)) -> f(X:S) 0.00/0.09 f(mark(X:S)) -> f(X:S) 0.00/0.09 g(active(X:S)) -> g(X:S) 0.00/0.09 g(mark(X:S)) -> g(X:S) 0.00/0.09 h(active(X:S)) -> h(X:S) 0.00/0.09 h(mark(X:S)) -> h(X:S) 0.00/0.09 mark(c(X:S)) -> active(c(X:S)) 0.00/0.09 mark(d(X:S)) -> active(d(X:S)) 0.00/0.09 mark(f(X:S)) -> active(f(mark(X:S))) 0.00/0.09 mark(g(X:S)) -> active(g(X:S)) 0.00/0.09 mark(h(X:S)) -> active(h(mark(X:S))) 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 There is no strongly connected component 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 EOF