TRS Equational pair #487092828

details

property	value
status	complete
benchmark	YWHM14_5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.0479361 seconds
cpu usage	0.053055
user time	0.025665
system time	0.02739
max virtual memory	113188.0
max residence set size	4112.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR x)
(THEORY 
(AC plus))
(RULES
f(x) -> plus(g(x),a)
plus(f(x),g(x)) -> plus(g(x),plus(g(x),g(x)))
)

Problem 1: 

Reduction Order Processor:
-> Rules:
 f(x) -> plus(g(x),a)
 plus(f(x),g(x)) -> plus(g(x),plus(g(x),g(x)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = 2.X + 1
[plus](X1,X2) = X1 + X2
[a] = 0
[g](X) = X

Problem 1: 

Reduction Order Processor:
-> Rules:
 plus(f(x),g(x)) -> plus(g(x),plus(g(x),g(x)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = 2.X + 2
[plus](X1,X2) = X1 + X2
[a] = 0
[g](X) = X

Problem 1: 

Dependency Pairs Processor:
-> FAxioms:
 PLUS(plus(x1,x2),x3) = PLUS(x1,plus(x2,x3))
 PLUS(x1,x2) = PLUS(x2,x1)
-> Pairs:
 Empty
-> EAxioms:
 plus(plus(x1,x2),x3) = plus(x1,plus(x2,x3))
 plus(x1,x2) = plus(x2,x1)
-> Rules:
 Empty
-> SRules:
 PLUS(plus(x1,x2),x3) -> PLUS(x1,x2)
 PLUS(x1,plus(x2,x3)) -> PLUS(x2,x3)

Problem 1: 

SCC Processor:
-> FAxioms:
 PLUS(plus(x1,x2),x3) = PLUS(x1,plus(x2,x3))
 PLUS(x1,x2) = PLUS(x2,x1)
-> Pairs:
 Empty
-> EAxioms:
 plus(plus(x1,x2),x3) = plus(x1,plus(x2,x3))
 plus(x1,x2) = plus(x2,x1)
-> Rules:
 Empty
-> SRules:
 PLUS(plus(x1,x2),x3) -> PLUS(x1,x2)
 PLUS(x1,plus(x2,x3)) -> PLUS(x2,x3)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

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