/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 v_NonEmpty:S x:S y:S z:S)
(RULES
f(f(x:S,y:S),z:S) -> f(x:S,f(y:S,z:S))
f(0,y:S) -> y:S
f(1,g(x:S,y:S)) -> x:S
f(2,g(x:S,y:S)) -> y:S
f(g(x:S,y:S),z:S) -> g(f(x:S,z:S),f(y:S,z:S))
f(i(x:S),y:S) -> i(x:S)
f(x:S,0) -> x:S
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(x:S,y:S),z:S) -> F(x:S,f(y:S,z:S))
 F(f(x:S,y:S),z:S) -> F(y:S,z:S)
 F(g(x:S,y:S),z:S) -> F(x:S,z:S)
 F(g(x:S,y:S),z:S) -> F(y:S,z:S)
-> Rules:
 f(f(x:S,y:S),z:S) -> f(x:S,f(y:S,z:S))
 f(0,y:S) -> y:S
 f(1,g(x:S,y:S)) -> x:S
 f(2,g(x:S,y:S)) -> y:S
 f(g(x:S,y:S),z:S) -> g(f(x:S,z:S),f(y:S,z:S))
 f(i(x:S),y:S) -> i(x:S)
 f(x:S,0) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(x:S,y:S),z:S) -> F(x:S,f(y:S,z:S))
 F(f(x:S,y:S),z:S) -> F(y:S,z:S)
 F(g(x:S,y:S),z:S) -> F(x:S,z:S)
 F(g(x:S,y:S),z:S) -> F(y:S,z:S)
-> Rules:
 f(f(x:S,y:S),z:S) -> f(x:S,f(y:S,z:S))
 f(0,y:S) -> y:S
 f(1,g(x:S,y:S)) -> x:S
 f(2,g(x:S,y:S)) -> y:S
 f(g(x:S,y:S),z:S) -> g(f(x:S,z:S),f(y:S,z:S))
 f(i(x:S),y:S) -> i(x:S)
 f(x:S,0) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(x:S,y:S),z:S) -> F(x:S,f(y:S,z:S))
 F(f(x:S,y:S),z:S) -> F(y:S,z:S)
 F(g(x:S,y:S),z:S) -> F(x:S,z:S)
 F(g(x:S,y:S),z:S) -> F(y:S,z:S)
->->-> Rules:
 f(f(x:S,y:S),z:S) -> f(x:S,f(y:S,z:S))
 f(0,y:S) -> y:S
 f(1,g(x:S,y:S)) -> x:S
 f(2,g(x:S,y:S)) -> y:S
 f(g(x:S,y:S),z:S) -> g(f(x:S,z:S),f(y:S,z:S))
 f(i(x:S),y:S) -> i(x:S)
 f(x:S,0) -> x:S

Problem 1: 

Subterm Processor:
-> Pairs:
 F(f(x:S,y:S),z:S) -> F(x:S,f(y:S,z:S))
 F(f(x:S,y:S),z:S) -> F(y:S,z:S)
 F(g(x:S,y:S),z:S) -> F(x:S,z:S)
 F(g(x:S,y:S),z:S) -> F(y:S,z:S)
-> Rules:
 f(f(x:S,y:S),z:S) -> f(x:S,f(y:S,z:S))
 f(0,y:S) -> y:S
 f(1,g(x:S,y:S)) -> x:S
 f(2,g(x:S,y:S)) -> y:S
 f(g(x:S,y:S),z:S) -> g(f(x:S,z:S),f(y:S,z:S))
 f(i(x:S),y:S) -> i(x:S)
 f(x:S,0) -> x:S
->Projection:
 pi(F) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(f(x:S,y:S),z:S) -> f(x:S,f(y:S,z:S))
 f(0,y:S) -> y:S
 f(1,g(x:S,y:S)) -> x:S
 f(2,g(x:S,y:S)) -> y:S
 f(g(x:S,y:S),z:S) -> g(f(x:S,z:S),f(y:S,z:S))
 f(i(x:S),y:S) -> i(x:S)
 f(x:S,0) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.