TRS Standard pair #487067604

details

property	value
status	complete
benchmark	#3.23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0390331 seconds
cpu usage	0.037131
user time	0.0182
system time	0.018931
max virtual memory	113188.0
max residence set size	4872.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
f(0,y:S) -> 0
f(s(x:S),y:S) -> f(f(x:S,y:S),y:S)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(0,y:S) -> 0
 f(s(x:S),y:S) -> f(f(x:S,y: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(s(x:S),y:S) -> F(f(x:S,y:S),y:S)
 F(s(x:S),y:S) -> F(x:S,y:S)
-> Rules:
 f(0,y:S) -> 0
 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S)

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(x:S),y:S) -> F(f(x:S,y:S),y:S)
 F(s(x:S),y:S) -> F(x:S,y:S)
-> Rules:
 f(0,y:S) -> 0
 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(x:S),y:S) -> F(f(x:S,y:S),y:S)
 F(s(x:S),y:S) -> F(x:S,y:S)
->->-> Rules:
 f(0,y:S) -> 0
 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S)

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(x:S),y:S) -> F(x:S,y:S)
-> Rules:
 f(0,y:S) -> 0
 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(x:S),y:S) -> F(x:S,y:S)
->->-> Rules:
 f(0,y:S) -> 0
 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(s(x:S),y:S) -> F(x:S,y:S)
-> Rules:
 f(0,y:S) -> 0
 f(s(x:S),y:S) -> f(f(x:S,y:S),y:S)
->Projection:

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