TRS Equational pair #487092741

details

property	value
status	complete
benchmark	AC02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.194345 seconds
cpu usage	0.197744
user time	0.105656
system time	0.092088
max virtual memory	113188.0
max residence set size	5004.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR x y)
(THEORY 
(AC plus))
(RULES
double(x) -> plus(x,x)
plus(x,0) -> x
plus(x,s(y)) -> s(plus(x,y))
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> FAxioms:
 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
 PLUS(x2,x3) = PLUS(x3,x2)
-> Pairs:
 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
 PLUS(plus(x,s(y)),x2) -> PLUS(x,y)
 PLUS(x,s(y)) -> PLUS(x,y)
-> EAxioms:
 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
 plus(x2,x3) = plus(x3,x2)
-> Rules:
 plus(x,s(y)) -> s(plus(x,y))
-> SRules:
 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)

Problem 1: 

SCC Processor:
-> FAxioms:
 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
 PLUS(x2,x3) = PLUS(x3,x2)
-> Pairs:
 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
 PLUS(plus(x,s(y)),x2) -> PLUS(x,y)
 PLUS(x,s(y)) -> PLUS(x,y)
-> EAxioms:
 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
 plus(x2,x3) = plus(x3,x2)
-> Rules:
 plus(x,s(y)) -> s(plus(x,y))
-> SRules:
 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
 PLUS(plus(x,s(y)),x2) -> PLUS(x,y)
 PLUS(x,s(y)) -> PLUS(x,y)
-> FAxioms:

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