/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR X Y Z)
(RULES
f(X,Y,g(X,Y)) -> h(0,g(X,Y))
g(0,Y) -> 0
g(X,s(Y)) -> g(X,Y)
h(X,Z) -> f(X,s(X),Z)
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(X,Y,g(X,Y)) -> H(0,g(X,Y))
 G(X,s(Y)) -> G(X,Y)
 H(X,Z) -> F(X,s(X),Z)
-> Rules:
 f(X,Y,g(X,Y)) -> h(0,g(X,Y))
 g(0,Y) -> 0
 g(X,s(Y)) -> g(X,Y)
 h(X,Z) -> f(X,s(X),Z)

Problem 1: 

SCC Processor:
-> Pairs:
 F(X,Y,g(X,Y)) -> H(0,g(X,Y))
 G(X,s(Y)) -> G(X,Y)
 H(X,Z) -> F(X,s(X),Z)
-> Rules:
 f(X,Y,g(X,Y)) -> h(0,g(X,Y))
 g(0,Y) -> 0
 g(X,s(Y)) -> g(X,Y)
 h(X,Z) -> f(X,s(X),Z)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(X,s(Y)) -> G(X,Y)
->->-> Rules:
 f(X,Y,g(X,Y)) -> h(0,g(X,Y))
 g(0,Y) -> 0
 g(X,s(Y)) -> g(X,Y)
 h(X,Z) -> f(X,s(X),Z)

Problem 1: 

Subterm Processor:
-> Pairs:
 G(X,s(Y)) -> G(X,Y)
-> Rules:
 f(X,Y,g(X,Y)) -> h(0,g(X,Y))
 g(0,Y) -> 0
 g(X,s(Y)) -> g(X,Y)
 h(X,Z) -> f(X,s(X),Z)
->Projection:
 pi(G) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(X,Y,g(X,Y)) -> h(0,g(X,Y))
 g(0,Y) -> 0
 g(X,s(Y)) -> g(X,Y)
 h(X,Z) -> f(X,s(X),Z)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.