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TRS Standard pair #487066919
details
property
value
status
complete
benchmark
#4.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n185.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.049943 seconds
cpu usage
0.039571
user time
0.01508
system time
0.024491
max virtual memory
113188.0
max residence set size
5556.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> PLUS(z:S,s(0)) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,plus(z:S,s(0)),s(z:S)) -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) Problem 1: SCC Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> PLUS(z:S,s(0)) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,plus(z:S,s(0)),s(z:S)) -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) ->->-> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ->->Cycle: ->->-> Pairs: QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,plus(z:S,s(0)),s(z:S)) ->->-> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ->Projection: pi(PLUS) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S))
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