TRS Equat 89423 pair #381732669

details

property	value
status	complete
benchmark	AC27.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n098.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	19.0304369926 seconds
cpu usage	16.765392551
max memory	2.5260032E7

stage attributes

key	value
output-size	78561
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR t x y z)
(THEORY 
(AC app plus))
(RULES
app(singl(x),singl(y)) -> if(eq(x,y),singl(x),empty)
app(x,app(plus(y,z),t)) -> app(plus(app(x,y),app(x,z)),t)
app(x,app(empty,z)) -> app(empty,z)
app(x,plus(y,z)) -> plus(app(x,y),app(x,z))
app(x,empty) -> empty
eq(0,0) -> true
eq(0,s(x)) -> false
eq(s(x),s(y)) -> eq(x,y)
if(false,x,y) -> y
if(true,x,y) -> x
plus(empty,x) -> x
)

Problem 1: 

Dependency Pairs Processor:
-> FAxioms:
 APP(app(x4,x5),x6) = APP(x4,app(x5,x6))
 APP(x4,x5) = APP(x5,x4)
 PLUS(plus(x4,x5),x6) = PLUS(x4,plus(x5,x6))
 PLUS(x4,x5) = PLUS(x5,x4)
-> Pairs:
 APP(app(singl(x),singl(y)),x4) -> APP(if(eq(x,y),singl(x),empty),x4)
 APP(app(singl(x),singl(y)),x4) -> EQ(x,y)
 APP(app(singl(x),singl(y)),x4) -> IF(eq(x,y),singl(x),empty)
 APP(app(x,app(plus(y,z),t)),x4) -> APP(app(plus(app(x,y),app(x,z)),t),x4)
 APP(app(x,app(plus(y,z),t)),x4) -> APP(plus(app(x,y),app(x,z)),t)
 APP(app(x,app(plus(y,z),t)),x4) -> APP(x,y)
 APP(app(x,app(plus(y,z),t)),x4) -> APP(x,z)
 APP(app(x,app(plus(y,z),t)),x4) -> PLUS(app(x,y),app(x,z))
 APP(app(x,app(empty,z)),x4) -> APP(app(empty,z),x4)
 APP(app(x,plus(y,z)),x4) -> APP(plus(app(x,y),app(x,z)),x4)
 APP(app(x,plus(y,z)),x4) -> APP(x,y)
 APP(app(x,plus(y,z)),x4) -> APP(x,z)
 APP(app(x,plus(y,z)),x4) -> PLUS(app(x,y),app(x,z))
 APP(app(x,empty),x4) -> APP(empty,x4)
 APP(singl(x),singl(y)) -> EQ(x,y)
 APP(singl(x),singl(y)) -> IF(eq(x,y),singl(x),empty)
 APP(x,app(plus(y,z),t)) -> APP(plus(app(x,y),app(x,z)),t)
 APP(x,app(plus(y,z),t)) -> APP(x,y)
 APP(x,app(plus(y,z),t)) -> APP(x,z)
 APP(x,app(plus(y,z),t)) -> PLUS(app(x,y),app(x,z))
 APP(x,plus(y,z)) -> APP(x,y)
 APP(x,plus(y,z)) -> APP(x,z)
 APP(x,plus(y,z)) -> PLUS(app(x,y),app(x,z))
 EQ(s(x),s(y)) -> EQ(x,y)
 PLUS(plus(empty,x),x4) -> PLUS(x,x4)
-> EAxioms:
 app(app(x4,x5),x6) = app(x4,app(x5,x6))
 app(x4,x5) = app(x5,x4)
 plus(plus(x4,x5),x6) = plus(x4,plus(x5,x6))
 plus(x4,x5) = plus(x5,x4)
-> Rules:
 app(singl(x),singl(y)) -> if(eq(x,y),singl(x),empty)
 app(x,app(plus(y,z),t)) -> app(plus(app(x,y),app(x,z)),t)
 app(x,app(empty,z)) -> app(empty,z)
 app(x,plus(y,z)) -> plus(app(x,y),app(x,z))
 app(x,empty) -> empty
 eq(0,0) -> true
 eq(0,s(x)) -> false
 eq(s(x),s(y)) -> eq(x,y)
 if(false,x,y) -> y
 if(true,x,y) -> x
 plus(empty,x) -> x
-> SRules:
 APP(app(x4,x5),x6) -> APP(x4,x5)
 APP(x4,app(x5,x6)) -> APP(x5,x6)
 PLUS(plus(x4,x5),x6) -> PLUS(x4,x5)
 PLUS(x4,plus(x5,x6)) -> PLUS(x5,x6)

Problem 1: 

SCC Processor:
-> FAxioms:
 APP(app(x4,x5),x6) = APP(x4,app(x5,x6))
 APP(x4,x5) = APP(x5,x4)
 PLUS(plus(x4,x5),x6) = PLUS(x4,plus(x5,x6))
 PLUS(x4,x5) = PLUS(x5,x4)
-> Pairs:
 APP(app(singl(x),singl(y)),x4) -> APP(if(eq(x,y),singl(x),empty),x4)
 APP(app(singl(x),singl(y)),x4) -> EQ(x,y)
 APP(app(singl(x),singl(y)),x4) -> IF(eq(x,y),singl(x),empty)
 APP(app(x,app(plus(y,z),t)),x4) -> APP(app(plus(app(x,y),app(x,z)),t),x4)
 APP(app(x,app(plus(y,z),t)),x4) -> APP(plus(app(x,y),app(x,z)),t)
 APP(app(x,app(plus(y,z),t)),x4) -> APP(x,y)
 APP(app(x,app(plus(y,z),t)),x4) -> APP(x,z)

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