details

property	value
status	complete
benchmark	#3.2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.046736 seconds
cpu usage	0.038689
user time	0.017176
system time	0.021513
max virtual memory	113188.0
max residence set size	5472.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> pred(minus(x:S,y:S)) pred(s(x:S)) -> x: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: Innermost Equivalent Processor: -> Rules: minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> pred(minus(x:S,y:S)) pred(s(x:S)) -> x: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 term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: MINUS(x:S,s(y:S)) -> MINUS(x:S,y:S) MINUS(x:S,s(y:S)) -> PRED(minus(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(x:S,0) -> x:S minus(x:S,s(y:S)) -> pred(minus(x:S,y:S)) pred(s(x:S)) -> x: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(x:S,s(y:S)) -> MINUS(x:S,y:S) MINUS(x:S,s(y:S)) -> PRED(minus(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(x:S,0) -> x:S minus(x:S,s(y:S)) -> pred(minus(x:S,y:S)) pred(s(x:S)) -> x: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: MINUS(x:S,s(y:S)) -> MINUS(x:S,y:S) ->->-> Rules: minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> pred(minus(x:S,y:S)) pred(s(x:S)) -> x: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(x:S,0) -> x:S minus(x:S,s(y:S)) -> pred(minus(x:S,y:S)) pred(s(x:S)) -> x: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 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: MINUS(x:S,s(y:S)) -> MINUS(x:S,y:S) -> Rules: minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> pred(minus(x:S,y:S)) pred(s(x:S)) -> x:S quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) ->Projection: pi(MINUS) = 2 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> pred(minus(x:S,y:S)) pred(s(x:S)) -> x:S popout

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