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TRS Standard pair #487067462
details
property
value
status
complete
benchmark
#3.39.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
2.03843 seconds
cpu usage
6.83559
user time
5.46029
system time
1.37529
max virtual memory
6534116.0
max residence set size
87940.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0()))) Proof: DP Processor: DPs: minus#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) plus#(s(x),y) -> plus#(x,y) plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0()))) TDG Processor: DPs: minus#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) plus#(s(x),y) -> plus#(x,y) plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0()))) graph: plus#(s(x),y) -> plus#(x,y) -> plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y) plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) -> plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) -> plus#(s(x),y) -> plus#(x,y) quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) -> quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) -> quot#(s(x),s(y)) -> minus#(x,y) quot#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y) minus#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y) SCC Processor: #sccs: 3 #rules: 4 #arcs: 8/25 DPs: quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0()))) Subterm Criterion Processor: simple projection: pi(minus) = 0 pi(quot#) = 0 problem: DPs: TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0()))) Qed DPs: minus#(s(x),s(y)) -> minus#(x,y) TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0()))) Subterm Criterion Processor:
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