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TRS Equational pair #487092744
details
property
value
status
complete
benchmark
AC13.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)
7.42912 seconds
cpu usage
6.67495
user time
4.53881
system time
2.13614
max virtual memory
691168.0
max residence set size
10600.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR x y z) (THEORY (AC plus times)) (RULES i(i(x)) -> x i(plus(x,y)) -> plus(i(x),i(y)) i(0) -> 0 plus(x,i(x)) -> 0 plus(x,0) -> x times(x,i(y)) -> i(times(x,y)) times(x,plus(y,z)) -> plus(times(x,y),times(x,z)) times(x,0) -> 0 ) Problem 1: Dependency Pairs Processor: -> FAxioms: PLUS(plus(x3,x4),x5) = PLUS(x3,plus(x4,x5)) PLUS(x3,x4) = PLUS(x4,x3) TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5)) TIMES(x3,x4) = TIMES(x4,x3) -> Pairs: I(plus(x,y)) -> I(x) I(plus(x,y)) -> I(y) I(plus(x,y)) -> PLUS(i(x),i(y)) PLUS(plus(x,i(x)),x3) -> PLUS(0,x3) PLUS(plus(x,0),x3) -> PLUS(x,x3) TIMES(times(x,i(y)),x3) -> I(times(x,y)) TIMES(times(x,i(y)),x3) -> TIMES(i(times(x,y)),x3) TIMES(times(x,i(y)),x3) -> TIMES(x,y) TIMES(times(x,plus(y,z)),x3) -> PLUS(times(x,y),times(x,z)) TIMES(times(x,plus(y,z)),x3) -> TIMES(plus(times(x,y),times(x,z)),x3) TIMES(times(x,plus(y,z)),x3) -> TIMES(x,y) TIMES(times(x,plus(y,z)),x3) -> TIMES(x,z) TIMES(times(x,0),x3) -> TIMES(0,x3) TIMES(x,i(y)) -> I(times(x,y)) TIMES(x,i(y)) -> TIMES(x,y) TIMES(x,plus(y,z)) -> PLUS(times(x,y),times(x,z)) TIMES(x,plus(y,z)) -> TIMES(x,y) TIMES(x,plus(y,z)) -> TIMES(x,z) -> EAxioms: plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5)) plus(x3,x4) = plus(x4,x3) times(times(x3,x4),x5) = times(x3,times(x4,x5)) times(x3,x4) = times(x4,x3) -> Rules: i(i(x)) -> x i(plus(x,y)) -> plus(i(x),i(y)) i(0) -> 0 plus(x,i(x)) -> 0 plus(x,0) -> x times(x,i(y)) -> i(times(x,y)) times(x,plus(y,z)) -> plus(times(x,y),times(x,z)) times(x,0) -> 0 -> SRules: PLUS(plus(x3,x4),x5) -> PLUS(x3,x4) PLUS(x3,plus(x4,x5)) -> PLUS(x4,x5) TIMES(times(x3,x4),x5) -> TIMES(x3,x4) TIMES(x3,times(x4,x5)) -> TIMES(x4,x5) Problem 1: SCC Processor: -> FAxioms: PLUS(plus(x3,x4),x5) = PLUS(x3,plus(x4,x5)) PLUS(x3,x4) = PLUS(x4,x3) TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5)) TIMES(x3,x4) = TIMES(x4,x3) -> Pairs: I(plus(x,y)) -> I(x) I(plus(x,y)) -> I(y) I(plus(x,y)) -> PLUS(i(x),i(y)) PLUS(plus(x,i(x)),x3) -> PLUS(0,x3) PLUS(plus(x,0),x3) -> PLUS(x,x3) TIMES(times(x,i(y)),x3) -> I(times(x,y)) TIMES(times(x,i(y)),x3) -> TIMES(i(times(x,y)),x3) TIMES(times(x,i(y)),x3) -> TIMES(x,y) TIMES(times(x,plus(y,z)),x3) -> PLUS(times(x,y),times(x,z)) TIMES(times(x,plus(y,z)),x3) -> TIMES(plus(times(x,y),times(x,z)),x3) TIMES(times(x,plus(y,z)),x3) -> TIMES(x,y) TIMES(times(x,plus(y,z)),x3) -> TIMES(x,z) TIMES(times(x,0),x3) -> TIMES(0,x3) TIMES(x,i(y)) -> I(times(x,y)) TIMES(x,i(y)) -> TIMES(x,y) TIMES(x,plus(y,z)) -> PLUS(times(x,y),times(x,z)) TIMES(x,plus(y,z)) -> TIMES(x,y) TIMES(x,plus(y,z)) -> TIMES(x,z) -> EAxioms: plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5)) plus(x3,x4) = plus(x4,x3) times(times(x3,x4),x5) = times(x3,times(x4,x5)) times(x3,x4) = times(x4,x3) -> Rules: i(i(x)) -> x i(plus(x,y)) -> plus(i(x),i(y))
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