/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(c(x),x,y) -> c(y)
f(s(x),y,z) -> f(x,s(c(y)),c(z))
f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
g(x,y) -> x
g(x,y) -> y
) 
(STRATEGY INNERMOST)

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.