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TRS Standard pair #516960856
details
property
value
status
complete
benchmark
thiemann17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n079.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.704146146774 seconds
cpu usage
0.617030526
max memory
9220096.0
stage attributes
key
value
output-size
11312
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S b:S m:S n:S x:S y:S) (RULES empty(cons(n:S,x:S)) -> ffalse empty(nil) -> ttrue head(cons(n:S,x:S)) -> n:S if(ffalse,b:S,x:S) -> if2(b:S,x:S) if(ttrue,b:S,x:S) -> weight_undefined_error if2(ffalse,x:S) -> weight(sum(x:S,cons(0,tail(tail(x:S))))) if2(ttrue,x:S) -> head(x:S) sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S tail(cons(n:S,x:S)) -> x:S tail(nil) -> nil weight(x:S) -> if(empty(x:S),empty(tail(x:S)),x:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: empty(cons(n:S,x:S)) -> ffalse empty(nil) -> ttrue head(cons(n:S,x:S)) -> n:S if(ffalse,b:S,x:S) -> if2(b:S,x:S) if(ttrue,b:S,x:S) -> weight_undefined_error if2(ffalse,x:S) -> weight(sum(x:S,cons(0,tail(tail(x:S))))) if2(ttrue,x:S) -> head(x:S) sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S tail(cons(n:S,x:S)) -> x:S tail(nil) -> nil weight(x:S) -> if(empty(x:S),empty(tail(x:S)),x:S) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: IF(ffalse,b:S,x:S) -> IF2(b:S,x:S) IF2(ffalse,x:S) -> SUM(x:S,cons(0,tail(tail(x:S)))) IF2(ffalse,x:S) -> TAIL(tail(x:S)) IF2(ffalse,x:S) -> TAIL(x:S) IF2(ffalse,x:S) -> WEIGHT(sum(x:S,cons(0,tail(tail(x:S))))) IF2(ttrue,x:S) -> HEAD(x:S) SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) WEIGHT(x:S) -> EMPTY(tail(x:S)) WEIGHT(x:S) -> EMPTY(x:S) WEIGHT(x:S) -> IF(empty(x:S),empty(tail(x:S)),x:S) WEIGHT(x:S) -> TAIL(x:S) -> Rules: empty(cons(n:S,x:S)) -> ffalse empty(nil) -> ttrue head(cons(n:S,x:S)) -> n:S if(ffalse,b:S,x:S) -> if2(b:S,x:S) if(ttrue,b:S,x:S) -> weight_undefined_error if2(ffalse,x:S) -> weight(sum(x:S,cons(0,tail(tail(x:S))))) if2(ttrue,x:S) -> head(x:S) sum(cons(0,x:S),y:S) -> sum(x:S,y:S) sum(cons(s(n:S),x:S),cons(m:S,y:S)) -> sum(cons(n:S,x:S),cons(s(m:S),y:S)) sum(nil,y:S) -> y:S tail(cons(n:S,x:S)) -> x:S tail(nil) -> nil weight(x:S) -> if(empty(x:S),empty(tail(x:S)),x:S) Problem 1: SCC Processor: -> Pairs: IF(ffalse,b:S,x:S) -> IF2(b:S,x:S) IF2(ffalse,x:S) -> SUM(x:S,cons(0,tail(tail(x:S)))) IF2(ffalse,x:S) -> TAIL(tail(x:S)) IF2(ffalse,x:S) -> TAIL(x:S) IF2(ffalse,x:S) -> WEIGHT(sum(x:S,cons(0,tail(tail(x:S))))) IF2(ttrue,x:S) -> HEAD(x:S) SUM(cons(0,x:S),y:S) -> SUM(x:S,y:S) SUM(cons(s(n:S),x:S),cons(m:S,y:S)) -> SUM(cons(n:S,x:S),cons(s(m:S),y:S)) WEIGHT(x:S) -> EMPTY(tail(x:S)) WEIGHT(x:S) -> EMPTY(x:S) WEIGHT(x:S) -> IF(empty(x:S),empty(tail(x:S)),x:S) WEIGHT(x:S) -> TAIL(x:S) -> Rules: empty(cons(n:S,x:S)) -> ffalse empty(nil) -> ttrue head(cons(n:S,x:S)) -> n:S if(ffalse,b:S,x:S) -> if2(b:S,x:S) if(ttrue,b:S,x:S) -> weight_undefined_error
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