/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: minus(minus(x,y),z) -> minus(x,plus(y,z)) 2: minus(0(),y) -> 0() 3: minus(x,0()) -> x 4: minus(s(x),s(y)) -> minus(x,y) 5: plus(0(),y) -> y 6: plus(s(x),y) -> plus(x,s(y)) 7: plus(s(x),y) -> s(plus(y,x)) 8: zero(s(x)) -> false() 9: zero(0()) -> true() 10: p(s(x)) -> x 11: p(0()) -> 0() 12: div(x,y) -> quot(x,y,0()) 13: quot(s(x),s(y),z) -> quot(minus(p(ack(0(),x)),y),s(y),s(z)) 14: quot(0(),s(y),z) -> z 15: ack(0(),x) -> s(x) 16: ack(0(),x) -> plus(x,s(0())) 17: ack(s(x),0()) -> ack(x,s(0())) 18: ack(s(x),s(y)) -> ack(x,ack(s(x),y)) Number of strict rules: 18 Direct poly ... failed. Freezing ack 1: minus(minus(x,y),z) -> minus(x,plus(y,z)) 2: minus(0(),y) -> 0() 3: minus(x,0()) -> x 4: minus(s(x),s(y)) -> minus(x,y) 5: plus(0(),y) -> y 6: plus(s(x),y) -> plus(x,s(y)) 7: plus(s(x),y) -> s(plus(y,x)) 8: zero(s(x)) -> false() 9: zero(0()) -> true() 10: p(s(x)) -> x 11: p(0()) -> 0() 12: div(x,y) -> quot(x,y,0()) 13: quot(s(x),s(y),z) -> quot(minus(p(ack❆1_0(x)),y),s(y),s(z)) 14: quot(0(),s(y),z) -> z 15: ack❆1_0(x) -> s(x) 16: ack❆1_0(x) -> plus(x,s(0())) 17: ack❆1_s(x,0()) -> ack(x,s(0())) 18: ack❆1_s(x,s(y)) -> ack(x,ack❆1_s(x,y)) 19: ack(0(),_1) ->= ack❆1_0(_1) 20: ack(s(_1),_2) ->= ack❆1_s(_1,_2) Number of strict rules: 18 Direct poly ... failed. Dependency Pairs: #1: #plus(s(x),y) -> #plus(x,s(y)) #2: #quot(s(x),s(y),z) -> #quot(minus(p(ack❆1_0(x)),y),s(y),s(z)) #3: #quot(s(x),s(y),z) -> #minus(p(ack❆1_0(x)),y) #4: #quot(s(x),s(y),z) -> #p(ack❆1_0(x)) #5: #quot(s(x),s(y),z) -> #ack❆1_0(x) #6: #div(x,y) -> #quot(x,y,0()) #7: #ack(s(_1),_2) ->? #ack❆1_s(_1,_2) #8: #plus(s(x),y) -> #plus(y,x) #9: #ack❆1_s(x,0()) -> #ack(x,s(0())) #10: #ack(0(),_1) ->? #ack❆1_0(_1) #11: #ack❆1_0(x) -> #plus(x,s(0())) #12: #minus(minus(x,y),z) -> #minus(x,plus(y,z)) #13: #minus(minus(x,y),z) -> #plus(y,z) #14: #minus(s(x),s(y)) -> #minus(x,y) #15: #ack❆1_s(x,s(y)) -> #ack(x,ack❆1_s(x,y)) #16: #ack❆1_s(x,s(y)) -> #ack❆1_s(x,y) Number of SCCs: 4, DPs: 9 SCC { #1 #8 } Sum... succeeded. zero(x1) w: (0) #div(x1,x2) w: (0) s(x1) w: (1 + x1) minus(x1,x2) w: (0) ack(x1,x2) w: (0) #plus(x1,x2) w: (x2 + x1) false() w: (0) div(x1,x2) w: (0) #ack❆1_0(x1) w: (0) #p(x1) w: (0) true() w: (0) p(x1) w: (0) 0() w: (0) quot(x1,x2,x3) w: (0) #minus(x1,x2) w: (0) ack❆1_0(x1) w: (0) plus(x1,x2) w: (0) #ack(x1,x2) w: (0) ack❆1_s(x1,x2) w: (0) #ack❆1_s(x1,x2) w: (0) #quot(x1,x2,x3) w: (0) #zero(x1) w: (0) USABLE RULES: { } Removed DPs: #8 Number of SCCs: 4, DPs: 8 SCC { #1 } Sum... succeeded. zero(x1) w: (0) #div(x1,x2) w: (0) s(x1) w: (1 + x1) minus(x1,x2) w: (0) ack(x1,x2) w: (0) #plus(x1,x2) w: (x1) false() w: (0) div(x1,x2) w: (0) #ack❆1_0(x1) w: (0) #p(x1) w: (0) true() w: (0) p(x1) w: (0) 0() w: (0) quot(x1,x2,x3) w: (0) #minus(x1,x2) w: (0) ack❆1_0(x1) w: (0) plus(x1,x2) w: (0) #ack(x1,x2) w: (0) ack❆1_s(x1,x2) w: (0) #ack❆1_s(x1,x2) w: (0) #quot(x1,x2,x3) w: (0) #zero(x1) w: (0) USABLE RULES: { } Removed DPs: #1 Number of SCCs: 3, DPs: 7 SCC { #2 } Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... sum_sum_int,sum_neg... succeeded. zero(x1) w: (0, 0) #div(x1,x2) w: (0, 0) s(x1) w: (max{0, 86832 + x1_1}, -1) minus(x1,x2) w: (max{0, 1 + x1_1}, 0) ack(x1,x2) w: (0, 0) #plus(x1,x2) w: (0, 0) false() w: (0, 0) div(x1,x2) w: (0, 0) #ack❆1_0(x1) w: (0, 0) #p(x1) w: (0, 0) true() w: (0, 0) p(x1) w: (max{0, -46314 + x1_1}, 0) 0() w: (0, -1) quot(x1,x2,x3) w: (0, 0) #minus(x1,x2) w: (0, 0) ack❆1_0(x1) w: (max{0, 111907 + x1_1}, 0) plus(x1,x2) w: (max{0, 1 + x2_1 + x1_1}, 0) #ack(x1,x2) w: (0, 0) ack❆1_s(x1,x2) w: (0, 0) #ack❆1_s(x1,x2) w: (0, 0) #quot(x1,x2,x3) w: (max{0, -40520 + x2_1 + x1_1}, -869 + x2_2) #zero(x1) w: (0, 0) USABLE RULES: { 1..7 10 11 15 16 } Removed DPs: #2 Number of SCCs: 2, DPs: 6 SCC { #12 #14 } Sum... succeeded. zero(x1) w: (0) #div(x1,x2) w: (0) s(x1) w: (1 + x1) minus(x1,x2) w: (17679 + x2 + x1) ack(x1,x2) w: (0) #plus(x1,x2) w: (0) false() w: (0) div(x1,x2) w: (0) #ack❆1_0(x1) w: (0) #p(x1) w: (0) true() w: (0) p(x1) w: (x1) 0() w: (1) quot(x1,x2,x3) w: (0) #minus(x1,x2) w: (20976 + x2 + x1) ack❆1_0(x1) w: (0) plus(x1,x2) w: (14681 + x2 + x1) #ack(x1,x2) w: (0) ack❆1_s(x1,x2) w: (0) #ack❆1_s(x1,x2) w: (0) #quot(x1,x2,x3) w: (0) #zero(x1) w: (0) USABLE RULES: { 5..7 } Removed DPs: #12 #14 Number of SCCs: 1, DPs: 4 SCC { #7 #9 #15 #16 } Sum... succeeded. zero(x1) w: (0) #div(x1,x2) w: (0) s(x1) w: (2 + x1) minus(x1,x2) w: (34765 + x2 + x1) ack(x1,x2) w: (0) #plus(x1,x2) w: (0) false() w: (0) div(x1,x2) w: (0) #ack❆1_0(x1) w: (0) #p(x1) w: (0) true() w: (0) p(x1) w: (x1) 0() w: (1) quot(x1,x2,x3) w: (0) #minus(x1,x2) w: (20976) ack❆1_0(x1) w: (1) plus(x1,x2) w: (29873 + x1) #ack(x1,x2) w: (590 + x1) ack❆1_s(x1,x2) w: (1 + x2 + x1) #ack❆1_s(x1,x2) w: (591 + x1) #quot(x1,x2,x3) w: (0) #zero(x1) w: (0) USABLE RULES: { } Removed DPs: #7 #9 #15 Number of SCCs: 1, DPs: 1 SCC { #16 } Sum... succeeded. zero(x1) w: (0) #div(x1,x2) w: (0) s(x1) w: (2 + x1) minus(x1,x2) w: (34765 + x2 + x1) ack(x1,x2) w: (0) #plus(x1,x2) w: (0) false() w: (0) div(x1,x2) w: (0) #ack❆1_0(x1) w: (0) #p(x1) w: (0) true() w: (0) p(x1) w: (x1) 0() w: (12457) quot(x1,x2,x3) w: (0) #minus(x1,x2) w: (20976) ack❆1_0(x1) w: (1) plus(x1,x2) w: (2 + x1) #ack(x1,x2) w: (590) ack❆1_s(x1,x2) w: (868 + x2 + x1) #ack❆1_s(x1,x2) w: (591 + x2) #quot(x1,x2,x3) w: (0) #zero(x1) w: (0) USABLE RULES: { } Removed DPs: #16 Number of SCCs: 0, DPs: 0