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TRS Equational pair #487092726
details
property
value
status
complete
benchmark
AC20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
1.37228 seconds
cpu usage
1.18311
user time
0.705611
system time
0.477501
max virtual memory
547000.0
max residence set size
7000.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR x y) (THEORY (AC plus times)) (RULES div(0,s(y)) -> 0 div(s(x),s(y)) -> s(div(minus(x,y),s(y))) minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x plus(x,0) -> x plus(x,s(y)) -> s(plus(x,y)) times(x,0) -> 0 times(x,s(y)) -> plus(times(x,y),x) ) Problem 1: Dependency Pairs Processor: -> FAxioms: PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4)) PLUS(x2,x3) = PLUS(x3,x2) TIMES(times(x2,x3),x4) = TIMES(x2,times(x3,x4)) TIMES(x2,x3) = TIMES(x3,x2) -> Pairs: DIV(s(x),s(y)) -> DIV(minus(x,y),s(y)) DIV(s(x),s(y)) -> MINUS(x,y) MINUS(s(x),s(y)) -> MINUS(x,y) PLUS(plus(x,0),x2) -> PLUS(x,x2) 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) TIMES(times(x,0),x2) -> TIMES(0,x2) TIMES(times(x,s(y)),x2) -> PLUS(times(x,y),x) TIMES(times(x,s(y)),x2) -> TIMES(plus(times(x,y),x),x2) TIMES(times(x,s(y)),x2) -> TIMES(x,y) TIMES(x,s(y)) -> PLUS(times(x,y),x) TIMES(x,s(y)) -> TIMES(x,y) -> EAxioms: plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4)) plus(x2,x3) = plus(x3,x2) times(times(x2,x3),x4) = times(x2,times(x3,x4)) times(x2,x3) = times(x3,x2) -> Rules: div(0,s(y)) -> 0 div(s(x),s(y)) -> s(div(minus(x,y),s(y))) minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x plus(x,0) -> x plus(x,s(y)) -> s(plus(x,y)) times(x,0) -> 0 times(x,s(y)) -> plus(times(x,y),x) -> SRules: PLUS(plus(x2,x3),x4) -> PLUS(x2,x3) PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4) TIMES(times(x2,x3),x4) -> TIMES(x2,x3) TIMES(x2,times(x3,x4)) -> TIMES(x3,x4) Problem 1: SCC Processor: -> FAxioms: PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4)) PLUS(x2,x3) = PLUS(x3,x2) TIMES(times(x2,x3),x4) = TIMES(x2,times(x3,x4)) TIMES(x2,x3) = TIMES(x3,x2) -> Pairs: DIV(s(x),s(y)) -> DIV(minus(x,y),s(y)) DIV(s(x),s(y)) -> MINUS(x,y) MINUS(s(x),s(y)) -> MINUS(x,y) PLUS(plus(x,0),x2) -> PLUS(x,x2) 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) TIMES(times(x,0),x2) -> TIMES(0,x2) TIMES(times(x,s(y)),x2) -> PLUS(times(x,y),x) TIMES(times(x,s(y)),x2) -> TIMES(plus(times(x,y),x),x2) TIMES(times(x,s(y)),x2) -> TIMES(x,y) TIMES(x,s(y)) -> PLUS(times(x,y),x) TIMES(x,s(y)) -> TIMES(x,y) -> EAxioms: plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4)) plus(x2,x3) = plus(x3,x2) times(times(x2,x3),x4) = times(x2,times(x3,x4)) times(x2,x3) = times(x3,x2) -> Rules: div(0,s(y)) -> 0 div(s(x),s(y)) -> s(div(minus(x,y),s(y))) minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x plus(x,0) -> x plus(x,s(y)) -> s(plus(x,y)) times(x,0) -> 0 times(x,s(y)) -> plus(times(x,y),x) -> SRules: PLUS(plus(x2,x3),x4) -> PLUS(x2,x3) PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4) TIMES(times(x2,x3),x4) -> TIMES(x2,x3)
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