/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR x1)
(RULES
b(b(x1)) -> c(d(x1))
c(c(x1)) -> d(d(d(x1)))
c(x1) -> g(x1)
d(d(d(x1))) -> g(c(x1))
d(d(x1)) -> c(f(x1))
f(x1) -> a(g(x1))
g(g(x1)) -> b(c(x1))
g(x1) -> d(a(b(x1)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 B(b(x1)) -> C(d(x1))
 B(b(x1)) -> D(x1)
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> B(c(x1))
 G(g(x1)) -> C(x1)
 G(x1) -> B(x1)
 G(x1) -> D(a(b(x1)))
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))

Problem 1: 

SCC Processor:
-> Pairs:
 B(b(x1)) -> C(d(x1))
 B(b(x1)) -> D(x1)
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> B(c(x1))
 G(g(x1)) -> C(x1)
 G(x1) -> B(x1)
 G(x1) -> D(a(b(x1)))
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(b(x1)) -> C(d(x1))
 B(b(x1)) -> D(x1)
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> B(c(x1))
 G(g(x1)) -> C(x1)
 G(x1) -> B(x1)
->->-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(b(x1)) -> C(d(x1))
 B(b(x1)) -> D(x1)
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> B(c(x1))
 G(g(x1)) -> C(x1)
 G(x1) -> B(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
-> Usable rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 2
[c](X) = X + 2
[d](X) = X + 4/3
[f](X) = X
[g](X) = X + 2
[a](X) = 0
[B](X) = 1/3.X + 2/3
[C](X) = 1/3.X + 3/4
[D](X) = 1/3.X + 1/2
[F](X) = 1/3.X + 3/4
[G](X) = 1/3.X + 2/3

Problem 1: 

SCC Processor:
-> Pairs:
 B(b(x1)) -> D(x1)
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> B(c(x1))
 G(g(x1)) -> C(x1)
 G(x1) -> B(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(b(x1)) -> D(x1)
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> B(c(x1))
 G(g(x1)) -> C(x1)
 G(x1) -> B(x1)
->->-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(b(x1)) -> D(x1)
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> B(c(x1))
 G(g(x1)) -> C(x1)
 G(x1) -> B(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
-> Usable rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 3/2
[c](X) = X + 3/2
[d](X) = X + 1
[f](X) = 1/4.X + 1/4
[g](X) = X + 3/2
[a](X) = 0
[B](X) = 1/2.X
[C](X) = 1/2.X + 1
[D](X) = 1/2.X + 2/3
[F](X) = 1/2.X + 1/4
[G](X) = 1/2.X + 1/4

Problem 1: 

SCC Processor:
-> Pairs:
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> B(c(x1))
 G(g(x1)) -> C(x1)
 G(x1) -> B(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
->->-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 C(c(x1)) -> D(d(d(x1)))
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
-> Usable rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 3/4
[c](X) = X + 3/4
[d](X) = X + 1/2
[f](X) = 1/3.X
[g](X) = X + 3/4
[a](X) = 0
[C](X) = 4.X + 2
[D](X) = 4.X + 1/2
[F](X) = 4.X + 4/3
[G](X) = 4.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
->->-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 C(c(x1)) -> D(d(x1))
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
-> Usable rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 2
[c](X) = X + 2
[d](X) = X + 4/3
[f](X) = 0
[g](X) = X + 2
[a](X) = 0
[C](X) = 4.X + 2
[D](X) = 4.X + 1/3
[F](X) = 4.X + 2
[G](X) = 4.X + 4/3

Problem 1: 

SCC Processor:
-> Pairs:
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
->->-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 C(c(x1)) -> D(x1)
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
-> Usable rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 1
[c](X) = X + 1
[d](X) = X + 2/3
[f](X) = 3/4.X + 1/4
[g](X) = X + 1
[a](X) = 0
[C](X) = 2.X + 3
[D](X) = 2.X + 4
[F](X) = 2.X + 3/2
[G](X) = 2.X + 3/2

Problem 1: 

SCC Processor:
-> Pairs:
 C(x1) -> G(x1)
 D(d(d(x1))) -> C(x1)
 D(d(d(x1))) -> G(c(x1))
 D(d(x1)) -> C(f(x1))
 D(d(x1)) -> F(x1)
 F(x1) -> G(x1)
 G(g(x1)) -> C(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(x1) -> G(x1)
 G(g(x1)) -> C(x1)
->->-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))

Problem 1: 

Subterm Processor:
-> Pairs:
 C(x1) -> G(x1)
 G(g(x1)) -> C(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Projection:
 pi(C) = 1
 pi(G) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 C(x1) -> G(x1)
-> Rules:
 b(b(x1)) -> c(d(x1))
 c(c(x1)) -> d(d(d(x1)))
 c(x1) -> g(x1)
 d(d(d(x1))) -> g(c(x1))
 d(d(x1)) -> c(f(x1))
 f(x1) -> a(g(x1))
 g(g(x1)) -> b(c(x1))
 g(x1) -> d(a(b(x1)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.