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TRS Equational pair #487092723
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
n139.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
19.5292 seconds
cpu usage
18.0736
user time
13.9543
system time
4.11929
max virtual memory
707216.0
max residence set size
19400.0
stage attributes
key
value
starexec-result
YES
output
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) 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))
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