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TRS Equational pair #487092678
details
property
value
status
complete
benchmark
AC41.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.372776 seconds
cpu usage
0.338724
user time
0.191001
system time
0.147723
max virtual memory
113188.0
max residence set size
6044.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR x y z) (THEORY (AC plus)) (RULES minus(minus(x,y),z) -> minus(x,plus(y,z)) minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y)) -> 0 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) ) Problem 1: Dependency Pairs Processor: -> FAxioms: PLUS(plus(x3,x4),x5) = PLUS(x3,plus(x4,x5)) PLUS(x3,x4) = PLUS(x4,x3) -> Pairs: MINUS(minus(x,y),z) -> MINUS(x,plus(y,z)) MINUS(minus(x,y),z) -> PLUS(y,z) MINUS(s(x),s(y)) -> MINUS(x,y) PLUS(plus(0,y),x3) -> PLUS(y,x3) PLUS(plus(s(x),y),x3) -> PLUS(s(plus(x,y)),x3) PLUS(plus(s(x),y),x3) -> PLUS(x,y) PLUS(s(x),y) -> PLUS(x,y) QUOT(s(x),s(y)) -> MINUS(x,y) QUOT(s(x),s(y)) -> QUOT(minus(x,y),s(y)) -> EAxioms: plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5)) plus(x3,x4) = plus(x4,x3) -> Rules: minus(minus(x,y),z) -> minus(x,plus(y,z)) minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y)) -> 0 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) -> SRules: PLUS(plus(x3,x4),x5) -> PLUS(x3,x4) PLUS(x3,plus(x4,x5)) -> PLUS(x4,x5) Problem 1: SCC Processor: -> FAxioms: PLUS(plus(x3,x4),x5) = PLUS(x3,plus(x4,x5)) PLUS(x3,x4) = PLUS(x4,x3) -> Pairs: MINUS(minus(x,y),z) -> MINUS(x,plus(y,z)) MINUS(minus(x,y),z) -> PLUS(y,z) MINUS(s(x),s(y)) -> MINUS(x,y) PLUS(plus(0,y),x3) -> PLUS(y,x3) PLUS(plus(s(x),y),x3) -> PLUS(s(plus(x,y)),x3) PLUS(plus(s(x),y),x3) -> PLUS(x,y) PLUS(s(x),y) -> PLUS(x,y) QUOT(s(x),s(y)) -> MINUS(x,y) QUOT(s(x),s(y)) -> QUOT(minus(x,y),s(y)) -> EAxioms: plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5)) plus(x3,x4) = plus(x4,x3) -> Rules: minus(minus(x,y),z) -> minus(x,plus(y,z)) minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y)) -> 0 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) -> SRules: PLUS(plus(x3,x4),x5) -> PLUS(x3,x4) PLUS(x3,plus(x4,x5)) -> PLUS(x4,x5) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(plus(0,y),x3) -> PLUS(y,x3) PLUS(plus(s(x),y),x3) -> PLUS(s(plus(x,y)),x3) PLUS(plus(s(x),y),x3) -> PLUS(x,y) PLUS(s(x),y) -> PLUS(x,y) -> FAxioms: plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5)) plus(x3,x4) -> plus(x4,x3) PLUS(plus(x3,x4),x5) -> PLUS(x3,plus(x4,x5)) PLUS(x3,x4) -> PLUS(x4,x3) -> EAxioms: plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5)) plus(x3,x4) = plus(x4,x3) ->->-> Rules: minus(minus(x,y),z) -> minus(x,plus(y,z)) minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y)) -> 0
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