YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 4580 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 18 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 52 ms] (10) IntTRS (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (12) IntTRS (13) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Rules: l0(__const_11HAT0, __const_9HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(__const_11HATpost, __const_9HATpost, oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: oldX3HAT0 = oldX3HATpost && __const_9HAT0 = __const_9HATpost && __const_11HAT0 = __const_11HATpost && x1HATpost = oldX2HATpost && x0HATpost = 1 + oldX0HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x5 = x13 && x4 = x12 && x1 = x9 && x = x8 && x15 = 1 + x11 && x14 = x10 && x11 = x7 && x10 = x6 l4(x16, x17, x18, x19, x20, x21, x22, x23) -> l5(x24, x25, x26, x27, x28, x29, x30, x31) :|: x17 = x25 && x16 = x24 && x31 = x29 && x30 = x28 && x29 = x29 && x28 = x28 && x27 = x23 && x26 = x22 l3(x32, x33, x34, x35, x36, x37, x38, x39) -> l0(x40, x41, x42, x43, x44, x45, x46, x47) :|: x37 = x45 && x36 = x44 && x33 = x41 && x32 = x40 && x47 = x43 && x46 = x42 && 1 + x32 <= x43 && x43 = x39 && x42 = x38 l3(x48, x49, x50, x51, x52, x53, x54, x55) -> l2(x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x61 && x52 = x60 && x49 = x57 && x48 = x56 && x63 = x59 && x62 = x58 && x59 <= x48 && x59 = x55 && x58 = x54 l1(x64, x65, x66, x67, x68, x69, x70, x71) -> l4(x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x77 && x65 = x73 && x64 = x72 && x79 = x76 && x78 = x74 && 1 + x65 <= x74 && x76 = x76 && x75 = x71 && x74 = x70 l1(x80, x81, x82, x83, x84, x85, x86, x87) -> l3(x88, x89, x90, x91, x92, x93, x94, x95) :|: x85 = x93 && x84 = x92 && x81 = x89 && x80 = x88 && x95 = 3 && x94 = x90 && x90 <= x81 && x91 = x87 && x90 = x86 l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l1(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x97 = x105 && x96 = x104 && x111 = x108 && x110 = 0 && x108 = x108 && x107 = x103 && x106 = x102 l7(x112, x113, x114, x115, x116, x117, x118, x119) -> l6(x120, x121, x122, x123, x124, x125, x126, x127) :|: x113 = x121 && x112 = x120 && x127 = x125 && x126 = x124 && x125 = x125 && x124 = x124 && x123 = x119 && x122 = x118 l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l5(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l0(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 l7(x160, x161, x162, x163, x164, x165, x166, x167) -> l2(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 l7(x176, x177, x178, x179, x180, x181, x182, x183) -> l4(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x178 = x186 && x177 = x185 && x176 = x184 l7(x192, x193, x194, x195, x196, x197, x198, x199) -> l3(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200 l7(x208, x209, x210, x211, x212, x213, x214, x215) -> l1(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x212 = x220 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 l7(x224, x225, x226, x227, x228, x229, x230, x231) -> l6(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 l8(x240, x241, x242, x243, x244, x245, x246, x247) -> l7(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x244 = x252 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 Start term: l8(__const_11HAT0, __const_9HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(__const_11HAT0, __const_9HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(__const_11HATpost, __const_9HATpost, oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: oldX3HAT0 = oldX3HATpost && __const_9HAT0 = __const_9HATpost && __const_11HAT0 = __const_11HATpost && x1HATpost = oldX2HATpost && x0HATpost = 1 + oldX0HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x5 = x13 && x4 = x12 && x1 = x9 && x = x8 && x15 = 1 + x11 && x14 = x10 && x11 = x7 && x10 = x6 l4(x16, x17, x18, x19, x20, x21, x22, x23) -> l5(x24, x25, x26, x27, x28, x29, x30, x31) :|: x17 = x25 && x16 = x24 && x31 = x29 && x30 = x28 && x29 = x29 && x28 = x28 && x27 = x23 && x26 = x22 l3(x32, x33, x34, x35, x36, x37, x38, x39) -> l0(x40, x41, x42, x43, x44, x45, x46, x47) :|: x37 = x45 && x36 = x44 && x33 = x41 && x32 = x40 && x47 = x43 && x46 = x42 && 1 + x32 <= x43 && x43 = x39 && x42 = x38 l3(x48, x49, x50, x51, x52, x53, x54, x55) -> l2(x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x61 && x52 = x60 && x49 = x57 && x48 = x56 && x63 = x59 && x62 = x58 && x59 <= x48 && x59 = x55 && x58 = x54 l1(x64, x65, x66, x67, x68, x69, x70, x71) -> l4(x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x77 && x65 = x73 && x64 = x72 && x79 = x76 && x78 = x74 && 1 + x65 <= x74 && x76 = x76 && x75 = x71 && x74 = x70 l1(x80, x81, x82, x83, x84, x85, x86, x87) -> l3(x88, x89, x90, x91, x92, x93, x94, x95) :|: x85 = x93 && x84 = x92 && x81 = x89 && x80 = x88 && x95 = 3 && x94 = x90 && x90 <= x81 && x91 = x87 && x90 = x86 l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l1(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x97 = x105 && x96 = x104 && x111 = x108 && x110 = 0 && x108 = x108 && x107 = x103 && x106 = x102 l7(x112, x113, x114, x115, x116, x117, x118, x119) -> l6(x120, x121, x122, x123, x124, x125, x126, x127) :|: x113 = x121 && x112 = x120 && x127 = x125 && x126 = x124 && x125 = x125 && x124 = x124 && x123 = x119 && x122 = x118 l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l5(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l0(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 l7(x160, x161, x162, x163, x164, x165, x166, x167) -> l2(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 l7(x176, x177, x178, x179, x180, x181, x182, x183) -> l4(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x178 = x186 && x177 = x185 && x176 = x184 l7(x192, x193, x194, x195, x196, x197, x198, x199) -> l3(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200 l7(x208, x209, x210, x211, x212, x213, x214, x215) -> l1(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x212 = x220 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 l7(x224, x225, x226, x227, x228, x229, x230, x231) -> l6(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 l8(x240, x241, x242, x243, x244, x245, x246, x247) -> l7(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x244 = x252 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 Start term: l8(__const_11HAT0, __const_9HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__const_11HAT0, __const_9HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(__const_11HATpost, __const_9HATpost, oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: oldX3HAT0 = oldX3HATpost && __const_9HAT0 = __const_9HATpost && __const_11HAT0 = __const_11HATpost && x1HATpost = oldX2HATpost && x0HATpost = 1 + oldX0HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 (2) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x5 = x13 && x4 = x12 && x1 = x9 && x = x8 && x15 = 1 + x11 && x14 = x10 && x11 = x7 && x10 = x6 (3) l4(x16, x17, x18, x19, x20, x21, x22, x23) -> l5(x24, x25, x26, x27, x28, x29, x30, x31) :|: x17 = x25 && x16 = x24 && x31 = x29 && x30 = x28 && x29 = x29 && x28 = x28 && x27 = x23 && x26 = x22 (4) l3(x32, x33, x34, x35, x36, x37, x38, x39) -> l0(x40, x41, x42, x43, x44, x45, x46, x47) :|: x37 = x45 && x36 = x44 && x33 = x41 && x32 = x40 && x47 = x43 && x46 = x42 && 1 + x32 <= x43 && x43 = x39 && x42 = x38 (5) l3(x48, x49, x50, x51, x52, x53, x54, x55) -> l2(x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x61 && x52 = x60 && x49 = x57 && x48 = x56 && x63 = x59 && x62 = x58 && x59 <= x48 && x59 = x55 && x58 = x54 (6) l1(x64, x65, x66, x67, x68, x69, x70, x71) -> l4(x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x77 && x65 = x73 && x64 = x72 && x79 = x76 && x78 = x74 && 1 + x65 <= x74 && x76 = x76 && x75 = x71 && x74 = x70 (7) l1(x80, x81, x82, x83, x84, x85, x86, x87) -> l3(x88, x89, x90, x91, x92, x93, x94, x95) :|: x85 = x93 && x84 = x92 && x81 = x89 && x80 = x88 && x95 = 3 && x94 = x90 && x90 <= x81 && x91 = x87 && x90 = x86 (8) l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l1(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x97 = x105 && x96 = x104 && x111 = x108 && x110 = 0 && x108 = x108 && x107 = x103 && x106 = x102 (9) l7(x112, x113, x114, x115, x116, x117, x118, x119) -> l6(x120, x121, x122, x123, x124, x125, x126, x127) :|: x113 = x121 && x112 = x120 && x127 = x125 && x126 = x124 && x125 = x125 && x124 = x124 && x123 = x119 && x122 = x118 (10) l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l5(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 (11) l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l0(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 (12) l7(x160, x161, x162, x163, x164, x165, x166, x167) -> l2(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 (13) l7(x176, x177, x178, x179, x180, x181, x182, x183) -> l4(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x178 = x186 && x177 = x185 && x176 = x184 (14) l7(x192, x193, x194, x195, x196, x197, x198, x199) -> l3(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200 (15) l7(x208, x209, x210, x211, x212, x213, x214, x215) -> l1(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x212 = x220 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 (16) l7(x224, x225, x226, x227, x228, x229, x230, x231) -> l6(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 (17) l8(x240, x241, x242, x243, x244, x245, x246, x247) -> l7(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x244 = x252 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 Arcs: (1) -> (6), (7) (2) -> (4), (5) (4) -> (1) (5) -> (2) (6) -> (3) (7) -> (4), (5) (8) -> (6), (7) (9) -> (8) (11) -> (1) (12) -> (2) (13) -> (3) (14) -> (4), (5) (15) -> (6), (7) (16) -> (8) (17) -> (9), (10), (11), (12), (13), (14), (15), (16) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(__const_11HAT0, __const_9HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(__const_11HATpost, __const_9HATpost, oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: oldX3HAT0 = oldX3HATpost && __const_9HAT0 = __const_9HATpost && __const_11HAT0 = __const_11HATpost && x1HATpost = oldX2HATpost && x0HATpost = 1 + oldX0HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 (2) l3(x32, x33, x34, x35, x36, x37, x38, x39) -> l0(x40, x41, x42, x43, x44, x45, x46, x47) :|: x37 = x45 && x36 = x44 && x33 = x41 && x32 = x40 && x47 = x43 && x46 = x42 && 1 + x32 <= x43 && x43 = x39 && x42 = x38 (3) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x5 = x13 && x4 = x12 && x1 = x9 && x = x8 && x15 = 1 + x11 && x14 = x10 && x11 = x7 && x10 = x6 (4) l3(x48, x49, x50, x51, x52, x53, x54, x55) -> l2(x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x61 && x52 = x60 && x49 = x57 && x48 = x56 && x63 = x59 && x62 = x58 && x59 <= x48 && x59 = x55 && x58 = x54 (5) l1(x80, x81, x82, x83, x84, x85, x86, x87) -> l3(x88, x89, x90, x91, x92, x93, x94, x95) :|: x85 = x93 && x84 = x92 && x81 = x89 && x80 = x88 && x95 = 3 && x94 = x90 && x90 <= x81 && x91 = x87 && x90 = x86 Arcs: (1) -> (5) (2) -> (1) (3) -> (2), (4) (4) -> (3) (5) -> (2), (4) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l3(__const_11HATpost:0, __const_9HATpost:0, x34:0, x35:0, x36:0, oldX3HATpost:0, oldX0HATpost:0, oldX1HATpost:0) -> l3(__const_11HATpost:0, __const_9HATpost:0, 1 + oldX0HATpost:0, oldX2HATpost:0, oldX2HATpost:0, oldX3HATpost:0, 1 + oldX0HATpost:0, 3) :|: oldX1HATpost:0 >= 1 + __const_11HATpost:0 && __const_9HATpost:0 >= 1 + oldX0HATpost:0 l3(x48:0, x49:0, x50:0, x51:0, x12:0, x13:0, x10:0, x11:0) -> l3(x48:0, x49:0, x10:0, x11:0, x12:0, x13:0, x10:0, 1 + x11:0) :|: x48:0 >= x11:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l3(x1, x2, x3, x4, x5, x6, x7, x8) -> l3(x1, x2, x7, x8) ---------------------------------------- (8) Obligation: Rules: l3(__const_11HATpost:0, __const_9HATpost:0, oldX0HATpost:0, oldX1HATpost:0) -> l3(__const_11HATpost:0, __const_9HATpost:0, 1 + oldX0HATpost:0, 3) :|: oldX1HATpost:0 >= 1 + __const_11HATpost:0 && __const_9HATpost:0 >= 1 + oldX0HATpost:0 l3(x48:0, x49:0, x10:0, x11:0) -> l3(x48:0, x49:0, x10:0, 1 + x11:0) :|: x48:0 >= x11:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l3(INTEGER, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l3(__const_11HATpost:0, __const_9HATpost:0, oldX0HATpost:0, oldX1HATpost:0) -> l3(__const_11HATpost:0, __const_9HATpost:0, c, c1) :|: c1 = 3 && c = 1 + oldX0HATpost:0 && (oldX1HATpost:0 >= 1 + __const_11HATpost:0 && __const_9HATpost:0 >= 1 + oldX0HATpost:0) l3(x48:0, x49:0, x10:0, x11:0) -> l3(x48:0, x49:0, x10:0, c2) :|: c2 = 1 + x11:0 && x48:0 >= x11:0 ---------------------------------------- (11) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l3(x, x1, x2, x3)] = -1 + x1 - x2 The following rules are decreasing: l3(__const_11HATpost:0, __const_9HATpost:0, oldX0HATpost:0, oldX1HATpost:0) -> l3(__const_11HATpost:0, __const_9HATpost:0, c, c1) :|: c1 = 3 && c = 1 + oldX0HATpost:0 && (oldX1HATpost:0 >= 1 + __const_11HATpost:0 && __const_9HATpost:0 >= 1 + oldX0HATpost:0) The following rules are bounded: l3(__const_11HATpost:0, __const_9HATpost:0, oldX0HATpost:0, oldX1HATpost:0) -> l3(__const_11HATpost:0, __const_9HATpost:0, c, c1) :|: c1 = 3 && c = 1 + oldX0HATpost:0 && (oldX1HATpost:0 >= 1 + __const_11HATpost:0 && __const_9HATpost:0 >= 1 + oldX0HATpost:0) ---------------------------------------- (12) Obligation: Rules: l3(x48:0, x49:0, x10:0, x11:0) -> l3(x48:0, x49:0, x10:0, c2) :|: c2 = 1 + x11:0 && x48:0 >= x11:0 ---------------------------------------- (13) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l3(x, x1, x2, x3)] = x - x3 The following rules are decreasing: l3(x48:0, x49:0, x10:0, x11:0) -> l3(x48:0, x49:0, x10:0, c2) :|: c2 = 1 + x11:0 && x48:0 >= x11:0 The following rules are bounded: l3(x48:0, x49:0, x10:0, x11:0) -> l3(x48:0, x49:0, x10:0, c2) :|: c2 = 1 + x11:0 && x48:0 >= x11:0 ---------------------------------------- (14) YES