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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.