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


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YES

Problem 1: 

(VAR x y z)
(RULES
f(0,1,x) -> f(s(x),x,x)
f(x,y,s(z)) -> s(f(0,1,z))
g(x,y) -> x
g(x,y) -> y
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(0,1,x) -> F(s(x),x,x)
 F(x,y,s(z)) -> F(0,1,z)
-> Rules:
 f(0,1,x) -> f(s(x),x,x)
 f(x,y,s(z)) -> s(f(0,1,z))
 g(x,y) -> x
 g(x,y) -> y

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,1,x) -> F(s(x),x,x)
 F(x,y,s(z)) -> F(0,1,z)
-> Rules:
 f(0,1,x) -> f(s(x),x,x)
 f(x,y,s(z)) -> s(f(0,1,z))
 g(x,y) -> x
 g(x,y) -> y
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,1,x) -> F(s(x),x,x)
 F(x,y,s(z)) -> F(0,1,z)
->->-> Rules:
 f(0,1,x) -> f(s(x),x,x)
 f(x,y,s(z)) -> s(f(0,1,z))
 g(x,y) -> x
 g(x,y) -> y

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,1,x) -> F(s(x),x,x)
 F(x,y,s(z)) -> F(0,1,z)
-> Rules:
 f(0,1,x) -> f(s(x),x,x)
 f(x,y,s(z)) -> s(f(0,1,z))
 g(x,y) -> x
 g(x,y) -> y
->Projection:
 pi(F) = 3

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,1,x) -> F(s(x),x,x)
-> Rules:
 f(0,1,x) -> f(s(x),x,x)
 f(x,y,s(z)) -> s(f(0,1,z))
 g(x,y) -> x
 g(x,y) -> y
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.