/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 v_NonEmpty:S x:S y:S z:S)
(RULES
f(0,1,x:S) -> f(s(x:S),x:S,x:S)
f(x:S,y:S,s(z:S)) -> s(f(0,1,z:S))
g(x:S,y:S) -> x:S
g(x:S,y:S) -> y:S
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.