YES

Problem 1: 

(VAR v_NonEmpty:S X:S)
(RULES
active(c(X:S)) -> mark(d(X:S))
active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
active(h(X:S)) -> mark(c(d(X:S)))
c(active(X:S)) -> c(X:S)
c(mark(X:S)) -> c(X:S)
d(active(X:S)) -> d(X:S)
d(mark(X:S)) -> d(X:S)
f(active(X:S)) -> f(X:S)
f(mark(X:S)) -> f(X:S)
g(active(X:S)) -> g(X:S)
g(mark(X:S)) -> g(X:S)
h(active(X:S)) -> h(X:S)
h(mark(X:S)) -> h(X:S)
mark(c(X:S)) -> active(c(X:S))
mark(d(X:S)) -> active(d(X:S))
mark(f(X:S)) -> active(f(mark(X:S)))
mark(g(X:S)) -> active(g(X:S))
mark(h(X:S)) -> active(h(mark(X:S)))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVE(c(X:S)) -> D(X:S)
 ACTIVE(c(X:S)) -> MARK(d(X:S))
 ACTIVE(f(f(X:S))) -> C(f(g(f(X:S))))
 ACTIVE(f(f(X:S))) -> F(g(f(X:S)))
 ACTIVE(f(f(X:S))) -> G(f(X:S))
 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S)))))
 ACTIVE(h(X:S)) -> C(d(X:S))
 ACTIVE(h(X:S)) -> D(X:S)
 ACTIVE(h(X:S)) -> MARK(c(d(X:S)))
 C(active(X:S)) -> C(X:S)
 C(mark(X:S)) -> C(X:S)
 D(active(X:S)) -> D(X:S)
 D(mark(X:S)) -> D(X:S)
 F(active(X:S)) -> F(X:S)
 F(mark(X:S)) -> F(X:S)
 G(active(X:S)) -> G(X:S)
 G(mark(X:S)) -> G(X:S)
 H(active(X:S)) -> H(X:S)
 H(mark(X:S)) -> H(X:S)
 MARK(c(X:S)) -> ACTIVE(c(X:S))
 MARK(d(X:S)) -> ACTIVE(d(X:S))
 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
 MARK(f(X:S)) -> F(mark(X:S))
 MARK(f(X:S)) -> MARK(X:S)
 MARK(g(X:S)) -> ACTIVE(g(X:S))
 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
 MARK(h(X:S)) -> H(mark(X:S))
 MARK(h(X:S)) -> MARK(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVE(c(X:S)) -> D(X:S)
 ACTIVE(c(X:S)) -> MARK(d(X:S))
 ACTIVE(f(f(X:S))) -> C(f(g(f(X:S))))
 ACTIVE(f(f(X:S))) -> F(g(f(X:S)))
 ACTIVE(f(f(X:S))) -> G(f(X:S))
 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S)))))
 ACTIVE(h(X:S)) -> C(d(X:S))
 ACTIVE(h(X:S)) -> D(X:S)
 ACTIVE(h(X:S)) -> MARK(c(d(X:S)))
 C(active(X:S)) -> C(X:S)
 C(mark(X:S)) -> C(X:S)
 D(active(X:S)) -> D(X:S)
 D(mark(X:S)) -> D(X:S)
 F(active(X:S)) -> F(X:S)
 F(mark(X:S)) -> F(X:S)
 G(active(X:S)) -> G(X:S)
 G(mark(X:S)) -> G(X:S)
 H(active(X:S)) -> H(X:S)
 H(mark(X:S)) -> H(X:S)
 MARK(c(X:S)) -> ACTIVE(c(X:S))
 MARK(d(X:S)) -> ACTIVE(d(X:S))
 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
 MARK(f(X:S)) -> F(mark(X:S))
 MARK(f(X:S)) -> MARK(X:S)
 MARK(g(X:S)) -> ACTIVE(g(X:S))
 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
 MARK(h(X:S)) -> H(mark(X:S))
 MARK(h(X:S)) -> MARK(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 H(active(X:S)) -> H(X:S)
 H(mark(X:S)) -> H(X:S)
->->-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->->Cycle:
->->-> Pairs:
 G(active(X:S)) -> G(X:S)
 G(mark(X:S)) -> G(X:S)
->->-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->->Cycle:
->->-> Pairs:
 F(active(X:S)) -> F(X:S)
 F(mark(X:S)) -> F(X:S)
->->-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->->Cycle:
->->-> Pairs:
 D(active(X:S)) -> D(X:S)
 D(mark(X:S)) -> D(X:S)
->->-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->->Cycle:
->->-> Pairs:
 C(active(X:S)) -> C(X:S)
 C(mark(X:S)) -> C(X:S)
->->-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->->Cycle:
->->-> Pairs:
 ACTIVE(c(X:S)) -> MARK(d(X:S))
 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S)))))
 ACTIVE(h(X:S)) -> MARK(c(d(X:S)))
 MARK(c(X:S)) -> ACTIVE(c(X:S))
 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
 MARK(f(X:S)) -> MARK(X:S)
 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
 MARK(h(X:S)) -> MARK(X:S)
->->-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))


The problem is decomposed in 6 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 H(active(X:S)) -> H(X:S)
 H(mark(X:S)) -> H(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Projection:
 pi(H) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 G(active(X:S)) -> G(X:S)
 G(mark(X:S)) -> G(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Projection:
 pi(G) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 F(active(X:S)) -> F(X:S)
 F(mark(X:S)) -> F(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Projection:
 pi(F) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Subterm Processor:
-> Pairs:
 D(active(X:S)) -> D(X:S)
 D(mark(X:S)) -> D(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Projection:
 pi(D) = 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.5: 

Subterm Processor:
-> Pairs:
 C(active(X:S)) -> C(X:S)
 C(mark(X:S)) -> C(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Projection:
 pi(C) = 1

Problem 1.5: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.6: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(c(X:S)) -> MARK(d(X:S))
 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S)))))
 ACTIVE(h(X:S)) -> MARK(c(d(X:S)))
 MARK(c(X:S)) -> ACTIVE(c(X:S))
 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
 MARK(f(X:S)) -> MARK(X:S)
 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
 MARK(h(X:S)) -> MARK(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
-> Usable rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[active](X) = X
[c](X) = 2
[d](X) = 0
[f](X) = 2.X + 1
[g](X) = 2.X + 2
[h](X) = 2.X + 2
[mark](X) = X
[fSNonEmpty] = 0
[ACTIVE](X) = 2.X
[C](X) = 0
[D](X) = 0
[F](X) = 0
[G](X) = 0
[H](X) = 0
[MARK](X) = 2.X

Problem 1.6: 

SCC Processor:
-> Pairs:
 ACTIVE(f(f(X:S))) -> MARK(c(f(g(f(X:S)))))
 ACTIVE(h(X:S)) -> MARK(c(d(X:S)))
 MARK(c(X:S)) -> ACTIVE(c(X:S))
 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
 MARK(f(X:S)) -> MARK(X:S)
 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
 MARK(h(X:S)) -> MARK(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(h(X:S)) -> MARK(c(d(X:S)))
 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
 MARK(f(X:S)) -> MARK(X:S)
 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
 MARK(h(X:S)) -> MARK(X:S)
->->-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))

Problem 1.6: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(h(X:S)) -> MARK(c(d(X:S)))
 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
 MARK(f(X:S)) -> MARK(X:S)
 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
 MARK(h(X:S)) -> MARK(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
-> Usable rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[active](X) = X
[c](X) = 0
[d](X) = 0
[f](X) = 2.X
[g](X) = 0
[h](X) = 2.X + 2
[mark](X) = 2.X
[fSNonEmpty] = 0
[ACTIVE](X) = X
[C](X) = 0
[D](X) = 0
[F](X) = 0
[G](X) = 0
[H](X) = 0
[MARK](X) = 2.X + 1

Problem 1.6: 

SCC Processor:
-> Pairs:
 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
 MARK(f(X:S)) -> MARK(X:S)
 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
 MARK(h(X:S)) -> MARK(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(f(X:S)) -> MARK(X:S)
 MARK(h(X:S)) -> MARK(X:S)
->->-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))

Problem 1.6: 

Subterm Processor:
-> Pairs:
 MARK(f(X:S)) -> MARK(X:S)
 MARK(h(X:S)) -> MARK(X:S)
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Projection:
 pi(MARK) = 1

Problem 1.6: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 active(c(X:S)) -> mark(d(X:S))
 active(f(f(X:S))) -> mark(c(f(g(f(X:S)))))
 active(h(X:S)) -> mark(c(d(X:S)))
 c(active(X:S)) -> c(X:S)
 c(mark(X:S)) -> c(X:S)
 d(active(X:S)) -> d(X:S)
 d(mark(X:S)) -> d(X:S)
 f(active(X:S)) -> f(X:S)
 f(mark(X:S)) -> f(X:S)
 g(active(X:S)) -> g(X:S)
 g(mark(X:S)) -> g(X:S)
 h(active(X:S)) -> h(X:S)
 h(mark(X:S)) -> h(X:S)
 mark(c(X:S)) -> active(c(X:S))
 mark(d(X:S)) -> active(d(X:S))
 mark(f(X:S)) -> active(f(mark(X:S)))
 mark(g(X:S)) -> active(g(X:S))
 mark(h(X:S)) -> active(h(mark(X:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.