TRS Standard pair #615306726

details

property	value
status	complete
benchmark	#4.37.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n059.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0605449676514 seconds
cpu usage	0.053155618
max memory	3141632.0

stage attributes

key	value
output-size	2727
starexec-result	"YES"

output

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


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


YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S)))
g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S)))
 g(c(x:S,s(y:S))) -> g(c(s(x:S),y: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(c(s(x:S),y:S)) -> F(c(x:S,s(y:S)))
 G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S))
-> Rules:
 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S)))
 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S))

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pairs Processor:
-> Pairs:
 G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S))
-> Rules:
 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S)))
 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = 0
[g](X) = 0
[c](X1,X2) = 2.X2
[fSNonEmpty] = 0
[s](X) = 2.X + 2
[F](X) = 0
[G](X) = 2.X

Problem 1.1: 

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

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