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TRS Standard pair #487067519
details
property
value
status
complete
benchmark
#3.4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0615559 seconds
cpu usage
0.041454
user time
0.019701
system time
0.021753
max virtual memory
113188.0
max residence set size
5576.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES minus(minus(x:S,y:S),z:S) -> minus(x:S,plus(y:S,z:S)) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) ) Problem 1: Dependency Pairs Processor: -> Pairs: MINUS(minus(x:S,y:S),z:S) -> MINUS(x:S,plus(y:S,z:S)) MINUS(minus(x:S,y:S),z:S) -> PLUS(y:S,z:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) QUOT(s(x:S),s(y:S)) -> MINUS(x:S,y:S) QUOT(s(x:S),s(y:S)) -> QUOT(minus(x:S,y:S),s(y:S)) -> Rules: minus(minus(x:S,y:S),z:S) -> minus(x:S,plus(y:S,z:S)) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) Problem 1: SCC Processor: -> Pairs: MINUS(minus(x:S,y:S),z:S) -> MINUS(x:S,plus(y:S,z:S)) MINUS(minus(x:S,y:S),z:S) -> PLUS(y:S,z:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) QUOT(s(x:S),s(y:S)) -> MINUS(x:S,y:S) QUOT(s(x:S),s(y:S)) -> QUOT(minus(x:S,y:S),s(y:S)) -> Rules: minus(minus(x:S,y:S),z:S) -> minus(x:S,plus(y:S,z:S)) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) ->->-> Rules: minus(minus(x:S,y:S),z:S) -> minus(x:S,plus(y:S,z:S)) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) ->->Cycle: ->->-> Pairs: MINUS(minus(x:S,y:S),z:S) -> MINUS(x:S,plus(y:S,z:S)) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) ->->-> Rules: minus(minus(x:S,y:S),z:S) -> minus(x:S,plus(y:S,z:S)) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) ->->Cycle: ->->-> Pairs: QUOT(s(x:S),s(y:S)) -> QUOT(minus(x:S,y:S),s(y:S)) ->->-> Rules: minus(minus(x:S,y:S),z:S) -> minus(x:S,plus(y:S,z:S)) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) -> Rules: minus(minus(x:S,y:S),z:S) -> minus(x:S,plus(y:S,z:S)) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S
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