TRS Standard pair #487069284

details

property	value
status	complete
benchmark	nestrec.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0560491 seconds
cpu usage	0.035685
user time	0.018727
system time	0.016958
max virtual memory	113188.0
max residence set size	4748.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR v_NonEmpty:S X:S)
(RULES
f(g(X:S)) -> g(f(f(X:S)))
f(h(X:S)) -> h(g(X:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(g(X:S)) -> F(f(X:S))
 F(g(X:S)) -> F(X:S)
-> Rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))

Problem 1: 

SCC Processor:
-> Pairs:
 F(g(X:S)) -> F(f(X:S))
 F(g(X:S)) -> F(X:S)
-> Rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(g(X:S)) -> F(f(X:S))
 F(g(X:S)) -> F(X:S)
->->-> Rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(g(X:S)) -> F(f(X:S))
 F(g(X:S)) -> F(X:S)
-> Rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))
-> Usable rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = X
[fSNonEmpty] = 0
[g](X) = 2.X + 2
[h](X) = 2
[F](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 F(g(X:S)) -> F(X:S)
-> Rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(g(X:S)) -> F(X:S)
->->-> Rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 F(g(X:S)) -> F(X:S)
-> Rules:
 f(g(X:S)) -> g(f(f(X:S)))
 f(h(X:S)) -> h(g(X:S))
->Projection:

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